This actually can work quite well. Done it a handful of times over the years. First, chill your bottles in the fridge, especially if your warm bottles want to throw beer. Give the beer a few days in the fridge, then crack one at serving temp before you pass judgment on the carb level.
One at a time, pop each cap and place a new sanitized cap on top of each bottle. As time passes and the bottles warm, CO2 comes out of solution into the headspace and pushes out under the loose cap.
How long to leave the bottles breathing before clamping down the new caps depends on a number of factors and ends up being your best guess. I've done as little as 10 minutes to around two hours with maybe a 20 degree temp increase over that time.
If you're dealing with some degree of foamer/gusher, it helps to weigh down the cap with a good size foil sheet umbrella to keep the cap from floating away on the wings of foam.
Finally and most importantly since this is all CO2 whispering and such (you don't really know how long it'll take to get the residual level you desire), do a test run or two. Vent two bottles, let breathe for 30 minutes at room temp (note the temp), cap down and then give them a few days for solution and headspace to equalize. Then refrigerate if not already and taste test.
Don't worry, no oxidation here. You're recapping on a regenerating CO2 headspace blanket.