What would an actor with a horrible signature do in this situation?

Hire a signature ghostwriter.

If you have a random signature, you could try making many of them until you see one you like, and then scan it (and/or make a stamp), for when that happens to you.

Famous persons often sign autographs differently than for documents. Prevention from forgery I suppose. So, many signatures don’t resemble the name at all.

For the movie, they would take their time & draw their name legibly. How tough is it to figure that one out?

Is there some sort of physical problem you have that your signature is very different every time? We are taught to develop a signature when we are young, and that we are going to have to stick with it eventually as we become adults.

Famous people sometimes have different signatures for autographs than legal documents, as @Patty_Melt mentioned.

It doesn’t matter if your signature is a mess, it matters that it is consistent.

You could refuse to do autographs.

In Florida if your signature is different every time they can reject your vote in political elections.