That'd be the thread, but you should also read up elsewhere online about how it works, and the differences between BCH and BTC.
Should be "safe" as long as you use Armory to split and make sure you sign with the BCH signer. Do not expose your private keys.

You asked for help. You're going to run into more problems down the line, as the network changes, if you don't update.

No, it'll still use your existing wallet. By default you can see your wallet files in "%appdata%\Armory" on Windows. Create a copy of that folder on the offline machine if you're really worried?

Nope, existing wallet - just update your preferences for receiving addresses and (potentially) your change address to use P2SH-P2WPKH (segwit - they'll start with a 3 rather than a 1).
Sending right now just to use segwit won't really save you on fees overall... so when fees drop to a level you are happy with send your existing coins over to segwit addresses in your wallet. For new coin purchases/transactions, you should send to a segwit address rather than the old format wherever possible.

As for the software upgrades, Bitcoin core on your online machine needs to have the segwit/witness flag - The latest does, but has been supported for a few versions now.
I'm going to quote a reply I made recently on this which is mostly relevant for you, but you really want to make sure you upgrade to > 0.96.3.99/0.96.4 RC1 from the pinned thread <. See below:

My single datapoint doesn't count for much but I managed to split my BCH successfully with 0.96.2 offline and 0.96.3 online, thanks to info in the sticky. Of course ideal world, or in case of any problems, matching is the route to take, with matching latest being even better

Unless you are worried it is compromised, you can continue to use your current wallet for segwit.
Ideally, you'll want Armory 0.96.3.99/0.96.4 RC1 and then change your preferences to use P2SH-P2WPKH (Segwit) in Armory. Change address too, perhaps but that is up to you regarding privacy.
I don't think upgrading Core is required, but the node rpc does need to be running on your full node. Offline machines with 0.96.4 RC1 can force segwit availability with --force-enable-segwit.

armory_0.96.2-ubuntu14.04-i386_offline.tar.gz might be worth trying too..? Though with caveats. Hoping they'll have any other dependencies already, for one, and not using segwit being another.

You quite likely need Armory 0.96.3.99/0.96.4 RC1 from the pinned thread.

This might help? Try that and attempt to send again. You may want to make sure you have Armory 0.96.3.99/0.96.4 RC1 from the pinned thread.

Bitcoin Core needs to be fully synced before Armory will show the balance. This requires ~160GB of storage space and will take a while.
You also need the correct version of Armory, not the version from the old site. See the sticky for 0.96.4 RC1.

Friendly heads up, you need to do your research instead of assuming everything will be alright and won't matter. It will likely bite you in the ass if you don't look into things more carefully in the future.

I think that just cleared it from Armory... and not from your node or the mempool. Which is not what you wanted to do.

The transaction is waiting to be confirmed in a block - heavy load on the network currently so depending on the fee you may be waiting a while.

You're pretty much there.
Test the heck out of your Trezor (with the multiple wallet types, I think?) and backups before migrating.
Send BTC and wait for it to confirm. Then BCH with the built in Armory signer.
For BTG, you'll need to import your private keys from Armory into another wallet in order to send it to the Trezor. Important to only do this after your BTC/BCH is safely migrated: Exposing your private keys is the dangerous part.
There is a lot of dubious bitcoin gold software out there too, so be safe and avoid taking the bait. The official Bitcoin Gold wallet was compromised at one point too!
Goatpig did post that he was working on a BTG signer, but I'm not sure if he was joking and I haven't read anything further since

Anything anyone else wants to add?

Pretty sure there are RBF fixes in Armory 0.96.4rc1/0.96.3.99. Try that?
edit: Scratch that. They're on the testing branch, not a released build. I guess either wait for an official build or build it yourself.

You can recover the coins if you have a printed backup somewhere. I'm guessing you don't?
You could try looking at the transaction dates to figure out when you would've taken the screenshot (of the QR code) then run searches on your various computers for an image file created during that time? Narrow it down by resolution perhaps too, depending.
Not much recourse for recovery though based on what you've said so far, but others might have some suggestions.

Time for Armory log files, I think.
File > Export Log File
Feel free to redact usernames as you did before for privacy's sake.

Save it and upload the contents to pastebin.com or another service.
I'm not a dev, so I probably won't notice much, but it will help goatpig/achow figure out what is going on.

No to the autoupdate. 15.1 is just under a month old. Did you mean 0.15.0.1? That has been around for a few months now
Regardless, Armory 0.96.4rc1/0.96.3.99 and Core 0.15.1 are the latest. Hopefully that should sort the db build issues.

Narrows it down a bit, thanks.
In Armory, have you tried Help > Rebuild and Rescan Databases ?
Hopefully it won't choke this time round. It does take a while to build the db from fresh.

To deal with the purple connected, you either need to add "-server" to your bitcoin core shortcut or "server=1" to a bitcoin.conf file in the bitcoin core data directory (i.e. usually on the same level as mempool.dat, peers.dat and so on). Will need to restart core for that to take effect.

Purple means the node RPC is not available. The bigger problem seems to be that you are ~470k blocks behind. Current block count is 498,147.
If you open bitcoin core, go to help > Debug Window. From there, on the "Information" tab look for "Current number of blocks" - what number is there?

Edit: And if your coins/transactions are more recent than 15th October 2009, they aren't going to appear without more blocks.

You could use rbf (replace by fee) to increase the fee, or just wait. A lot of network congestion at the moment with the current rally.

That is the latest.