Removing Riveted Metal Handles?

[SourRoses]

I know this is an odd question but I figured this is one of the best places to ask, with savvy people!

We have some really pretty handles on a really beat up pot & pan set (the non-stick coating did not endure). My mother was trying to throw the whole set away but I really want those handles. Not sure what I would use them for, but I'll find some purpose!

They are connected with rivets, rounded off inside the pan. Is there a way to get the rivets off without damaging the handles? My mother thought only an angle grinder would work, but I thought that sounds funky inside the rounded space of the pan interior, if that makes sense. Plus we don't have a grinder, lol. We do have a drill and some metal-worthy drill bits but I'm not sure how that would work...

Should I give up and throw the set away?

 

[wrathsfarm]

I've only ever drilled them out. If your able to use a center punch that would keep your bit from wandering.

A step bit might be useful also.

ETA...if you can't drill from outside, you could look at 90 degree drills or just an attachment, like this.

 

[aart]

They are connected with rivets, rounded off inside the pan.

Does the other end of the rivet show?
Pics would help here.

 

[Island Coppers]

Most of the rivets I've seen are chrome clad aluminum which is really soft. Use a punch to make spot on the rivet from the outside then use a larger bit to drill until you just reach the handle. It'll fall apart at that point.

 

[5Australorpasaures]

I've always used a punch or nail for a pilot and drilled them out. Sacrificed an old wood bit if a steel bit wasn't available.