Unfortunately I only own an old 4s with old iOS and none of the wallets are supported on my device. If I understand it correctly though I can just sweep my paper wallet with electrum to obtain my BTC keep the paper wallet aside get a cheap android phone in the future and sweep the BTG later right?
Yes, you can do that. Just write a note on the paper wallet: no Bitcoin left, only Bitcoin Gold (and BitCore). The list of forks gets longer, you may or may not have more forks on it already. It's hard to keep track what's real and what isn't nowadays.
I'm asking because I know I'm supposed to sweep all the coins on paper wallet otherwise the rest will be lost in the void so I don't know how it is with forked coins.
Forks are coins on a different chain, it shouldn't move when you move other coins (unless their replay protection fails, but so far that seems to be working just fine).
I googled for quite some time and I haven't find any legit looking BTG desktop wallet so I guess I'll just have to buy a new phone.
Coinomi says "coming soon" to iOS, but if your coins are worth it, an extra phone is a small investment. I'm paranoid with forked desktop wallets too.
I'm kinda reluctant to just sweep all my BTC to it.
Let me emphasize this again:
For safety, make sure your BTC is transfered and confirmed before importing your private keys into any other wallet.
Is it possible to sweep the BTC to my electrum desktop
Yes. There's no need to keep your Bitcoin on the paper wallets. You could of course just transfer them to a new (unused) paper wallet.
People have actually lost their Bitcoins trying to claim Bitcoin Gold through fake wallets/websites. There's absolutely no need to risk your Bitcoins, you can move them already and figure out how to use your Gold later.