Success!

Just following up to:

1) Thank everyone above for their time & input.

2) Let anyone else know in this conundrum that I did seemingly have to sync the entire blockchain after all before sending BTC out of Bitcoin Core. To save disk space, as advised, I went to Bitcoin Core > Preferences > checked the box for "Prune Block Storage to ____ GB" and arbitrarily chose 8GB. After about 4 days of syncing/downloading my transaction went through, and I can now send other transactions through as expected.

Thank you both so much for your time and suggestions.

BitMaxZ: I think I will try another transfer as you suggested. Just because I find this fee part a little confusing to calculate, I wanted to make sure I had the right idea.
Here's my screenshot example:

To summarize in text: if https://mempool.space was showing 49 sat/vB as "medium priority", I can enter in a fee of "0.00004900" BTC per Kilobyte in Bitcoin core? Is that correct? The other options are: mBTC, uBTC, Satoshi. I'm a little confused between how sat/vB translates to one of the available unit options.

Many thanks

Bitcoin Client Software and Version Number: Bitcoin Core v0.19.1 (64-bit)

Operating System: Yosemite 10.10.5

System Hardware Specs: 2009 Macbook Pro. ~30GB hard drive space free. 8GB RAM

Description of Problem: Trying to transfer a small amount of BTC I received in 2011 to my new Ledger Nano. I have confirmed the coin amount is still in the wallet. I started to let Bitcoin Core sync, but I don't have enough space to transfer the entire thing. I tried 2 test transfers, but cancelled after days of them being stuck. The first transaction had way too low a transfer fee (my mistake) and the 2nd I thought I had an accurate transfer rate (0.00103 BTC/kilobyte - a few days ago) but it was still stuck for several days before I cancelled the transaction.

Summary Questions:
        - What is the best method for me to transfer this old BTC to my new cold storage wallet/address?
        - Do I need to sync all of the blockchain before sending a transaction?
        - If yes to the above, can I "switch" the blockchain download/sync to an external SSD? or "switch" to make it start syncing in pruned mode?

Any specific steps would be greatly appreciated! Thank you.