What brakes (not levers) do you have that don't have a quick release mechanism?

Drop bar brake levers have a larger clamp diameter than standard mtb or flat bars, so there's more to the lever incompatibility than just lever shape/style.

Your brakes or levers (or both) should have barrel adjusters. Setting up the brakes so that you still have enough slack to widen the calipers via the adjusters for wheel removal is one possible workaround. Deflating/inflating is an effective, though annoying, last resort.