I lucked out. I haven't been able to find any spec sheet for the FH-A410 BUT Shimano does have a freehub interchangeability chart within which this listed.

The part # is Y3AP98020 which is also used in the FH-M290, FH-M330 and FH-MC32. I can get the part for about $17.

Should I push my luck and try to find some kind of a 8/9-speed version of this or just get this and be done with it?

I forgot about having the wheel this is on until I read that the Mavic MA rims that are on this wheelset have the same ERD as the Sun CR18 700c. I could repurpose these wheels for my beater bike and maybe also use these for touring.