I assume only BCH, BSV are probably worth the time.
As for BSV, your option for wallet and exchange would be very limited since it has ridiculous big blockchain size and so many controversy.
Are there any safe non-KYC exchanges where I can do the swaps?
No specific recommendation, but i'd mention
https://kycnot.me/ which list exchange with no or optional KYC.
Bitcoin Cash (BCH) and Bitcoin SV (BSV) are indeed the most notable forks of Bitcoin.
Actually BSV is fork of BCH. Although since OP haven't touched his coin in years, he should have both BCH and BSV.