It's not so much the sound but the spelling that makes it look so foreign to English speakers. But if it works with your surname, I think
Mikhail is fine :-) And I love its sound. Also
Mikhaila (mih-KYLE-a) for a girl. Apparently
Michaela can be pronounced that way - which makes more sense to me anyway - but you'd always get the wrong pronunciation :-(
I realise that
Mikayla is a Ukrainian name, but honestly I think that's incidental in the US, where it'll just be another take on
Makayla, Mackayla etc.
So yes, go ahead and use
Mikhail. But there might be other forms of
Michael that are pronounced the same way, so it's worth a bit of research.