A decent electrician will be able to install all the cans without drywall damage. I own a electrical company and we do this all the time. Last Mon. we fished 15 cans into a kitchen and dining area without any drywall damage. If you space your cans out properly you do not have to cut holes in the drywall to fish in the wires. You use the holes you cut for the cans to chase from joist space to joist space. If you have the proper tools it is easy. Proper knowledge is a bonus as well. Playing with electricity is not wise. Not to mention more and more insurance companies are voiding your homeowners insurance if it is found that work was done at the property without permits or licensed contractors doing the work. Not something you want to find out the day AFTER your house burns down. I always wondered if people who do their own electrical work do their own dental work as well? It takes 5 years to become an electrician, it is not something the idiot at home depot can explain to you while your loading your cart with wire.

If there's no pre-existing wiring, it will be a pretty nasty job. (Any junction boxes for splices must remain accessible.) If the ceiling is drywall affixed directly to the joists, you might consider just replacing the ceiling. You'd have to do a lot of cutting & patching and chances are it won't look good.

We did the same thing. What we did, was cut the holes for the cans, then made "trails" in the sheetrock between them to run the wiring. We then re-did the whole ceiling with 1/4" sheetrock. No worries about patching, or matching, and it was a lot easier than trying to do the job with "minimal intrusion" to avoid the "patching and matching".

How many lights are you installing? If it's several, it would be easier to make one large opening for access to the area. The patch can then be blended easily to the remaining area. When I had to do similar things, too small an area always caused delays and problems. Investigate the option of removing all of the ceiling material and putting up new sheet rock when you are done. Most kitchens would only need about 4 pieces of rock.