You can add the address in question as watched addresses in an online wallet,  then from that online wallet you can create a PSBT to spend the coins.

The PSBT can be brought to an offline computer, which has the private keys but no copy of the blockchain... and it can sign it.  Once signed, you can bring the result back online and transmit it.  (Ideally over TOR).

I think there is GUI support for PSBT now but I've only used it from the console myself now-- someone else will have to chime in there.  But I don't think you should be too afraid to use the console/command-line.  It looks a little more intimidating but its really the same steps and its usually easier to search for help about a text interface.

I know several people who use a procedure like this without trouble. 

You could practice doing it via testnet, which uses all the same software.

As far as breaking the connection on your coins-- that's a harder question.    You'd like to break the link to protect your identity, but the problem is that in doing so you might accidentally end up with coins whose history appears connected to something dubious and thereby attract attention to yourself that you wanted to avoid.


As far as wallet compatibility goes, fortunately there is no danger from the wallet: keep your original copy safe.  The worst that happens is that things don't work and you have some bug to report.


In any case, the biggest risk with any kind of manual transaction processing is accidentally turning your coins into fees usually due to a failure to understand that input coins that don't get given an output are implicitly fees.  Segwit and taproot outputs require the signer to sign the fees-- making things closer to fool proof, but your txouts are obviously not going to be segwit due to the age, so you should be sure to triple check that the amount of outputs adds up to the amount of the inputs minus the fees you intend.

The nice thing about a manual transaction flow is that you'll have the untransmitted transaction 'in hand' to review for as long as you want before you transmit it (or even bring it online).  You could show it to a friend or family member, or sleep on it to review the next day-- and I know people who do both of these things.