I don't think it makes a difference, or at least not one to worry about too much.
The spelling of one of my main domains should have an apostrophe in it. I didn't even think of it when I registered it. Most/many/some (pick one) users know that certain characters aren't allowed in domain names and are used to typing them that way as a matter of course. The ones who don't know really aren't quantifiable; if I can't count them, I can't worry about what I might be losing.
And if you look around I think you'll find many instances of the same type. Jim's this, Joe's that, etc. It's basically normal.
Considering you'll most likely use the apostrophe version of the name in the texts on your website, you shouldn't have a problem with search engines. Your domain name may not contain an apostrophe, but the text indexed by search engines does.
You can't use words with apostrophes in them in a domain name because it's against the protocol.
But some words...
... have an apostrophe in them!
So when you have a desired domain name which contains a word which contains an apostrophe, do you use it [minus the apostrophe] with all the orthographical error that entails, or do you avoid it in favour of another domain name?