i swap bows all the time for fun, and i only have the same batch of mismatched arrows to go along with them. I always shoot natural: never aim down the arrow, don't use peripheral vision: i just look at what i want to hit, draw, release. All my bows are about the same weight, within 12 # or so, and i find that even with one that has a wider handle, it only takes a shot or two for the body to figure it out.
The body, once trained, is smarter than me so i let it do the work!