Table leg foot repair help...

Daughter (no pics) moved into a new house, has an antique round table that has decorative wooden balls as feet attached to the legs. One of the balls was broken off in the move - its evident from the pics that ith has been jury rigged in the past as a quick fix. I'm not cheap, would be happy to pay a pro (or for her to pay a pro), but we live in a different city, so don't even know where to start with reputable shops. Daughter is a busy professional. Either taking it to a shop or coordinating with someone to come get it is difficult.

I think the solution to the problem is sand off the old glue where the ball is broken, drill a hole in the ball, and insert some type of threaded rod, and screw in a matching threaded insert into the table leg so it can be screwed back on securely.

I"m handy, but not a wood worker. There may be some specific set of screw or screws that fits this application, but google gave me way too many choices and I'd like to home in on something that is the actual right bit for the job. Any recs would be much appreciated.

I'm not cheap, would be happy to pay a pro (of for her to pay a pro), but I live in a different town. Daughter is a busy professional. Either taking it to a shop or coordinating with someone to come get it is difficult.