Can a handleset lock be replaced by a lock other than another handleset lock without making modifications to the hole?

A little more specifics about what you want to do please. There is a couple different sizes for the door knob or lock set , a couple sizes for the bolt and a couple for the back set (distance from the edge. Assuming you are speaking of standard entry or interior doors.

I have a handleset on my house that looks about 25 years old that is worn out and hard to use with the key. I would like to replace it with something more modern like a fingerprint or number combo lock. Thanks for any tips.

Having never installed a finger print or cipher (number combo) lock set, I can't help much, but you should be able to install. May require additional or larger holes but any modifications should be doable. Otherwise, they wouldn't sell many.

Suggest reading installation instructions before purchasing.