I have no keyboard and mouse to access my iMac

hey. I have an iMac bought in 2010 and I can't recall the last update. after returning from travelling in 2020 my keyboard and trackpad, which were unused for years (since 2016), the battery acid had leaked making them impossible to open up and replace batteries. So now I have no keyboard and mouse for my iMac and I can't access the machine.

I bought a cheap non-branded wireless keyboard but couldn't connect. Now I'm reluctant to buy an official apple one because I don't know what software my iMac is running and most keyboards require more recent software.

what can I do? I really want to get access to the machine but don't want to spend £100 on a keyboard to find it doesn't connect.

thank you

[Re-Titled by Moderator]