The best option, whether done by the carpenter or yourself, is to access the box from the backside of the wall... assuming the wall is just painted or wallpapered drywall, plasterboard, etc.. The biggest problem will if the box is metal and mounted with a front-of-stud bracket. To remove that box will require skilled use of a reciprocating saw with long metal blade, or an angle grinder with cutoff blade(s). Using either means, de-energize wires, remove from box, and bend back away from work area (assuming NM cable). It'll be much easier if the box used a side-of-stud bracket
Once the box (or what's left of it) is removed, and assuming you are putting a 4sq back in, make all your measurements and markings on the backside of the formica'd wall. Once you have the markings for the hole, measure off old hole then transfer to front side of wall and cut with oscillating tool using a metal cutting blade. Do not use heavy pressure on blade. Formica tends to be brittle from the start and gets more brittle with age. Let the blade "float" into the material. If there is wallboard behind the formica, use the oscillating tool with a very coarse tooth straight blade to hollow it out beyond the hole cut in the formica... from the backside.
Closing up the backside may present a challenge for some. If you are not good with wallboard repairs, have the homeowner bring her carpenter into the matter.