Your 7 wood head is, in all likelihood, heavier than your 3 wood head. The result of the union, between your 3 wood shaft and your 7 wood head, will be a longer club with more flex and a higher swing weight.
Look up the trimming instructions for the shaft in question. Some wood shafts are "butt trim only". That is not usually the case but one never knows...until one does. That will give you a better idea what you are getting into.
Also...weigh the heads. It is common practice, with tip-trimmed shafts, to trim an additional 1/2 inch from the tip for each 7 gram increase in head weight.
At any rate...bon chance.
I don’t have an official correct hcp at the moment but my garmin has me at 18,8. And if I see correctly it’s still a greenside bunker so the shot should be closer to 20 yards not 40? My bunker play is definitely better than my hcp would indicate. It very rarely happens that I don’t finish on the green from any greenside bunker shot. And a majority of the time I’m in easy 2 putt range.
I'm not quite sure this makes sense. Just because one shaft feels better on a certain club doesn't mean that it will feel just as good on a different club. I think a range session is in order for you, but I don't think that having a shaft longer than stock (assuming that you are of normal height), will be any kind of positive on that club. That's more of a long drive mentality.
Side note: swing weights are a thing, and if you mess with them, they can mess with you.