When I first got into bitcoin back in the day I used Multibit. I only ever had a small amount of bitcoin, but without going into too much detail I lost a few and ignored cryptocurrency for a while. When I regained interest I found that Multibit was no longer supported, so I sent my bitcoin to an Electrum wallet and subsequently moved to a hardware wallet.

I've just found out there may be a chance of regaining access to the bitcoin I lost back in the day if I can prove that the Multibit wallet was mine. I've been requested to make a small transaction from the same address of the Multibit wallet.

Could I deposit some bitcoin back to my Multibit wallet and send from there, or will there be issues? The max fees are 50k satoshi per kb - is that still sufficient today?

Alternatively, I still have old backups, including the .key .info and .wallet files from Multibit. Can I sweep/export these to another client? Are there problems/risks doing this with a .wallet file? Will I still have the same address if I try to sweep these to electrum?

Any help would be hugely appreciated. I don't have a huge amount but I'd be happy to help out anyone who can assist me.
Cheers