Should I do the same with my new gun and just shoot it to see how I get on?
Depends how close the new gun?s stock is to your present gun.
If they’re something of a match I would be inclined to use it straight out of the box and make a comparison only after putting a decent number of cartridges through it.
Who knows, you might actually shoot better with it than you managed with your previous gun!
Of course there’s always a chance your shooting goes the other way and if this does happen then don’t waste time ? get a gunsmith to have a good look at both stocks to see how they differ.
In this respect he will not just compare stock lengths and cast, he will want to check comb thickness as well as the shape and nature of the grip.
He will also want to check both guns for point of aim because if they are different additional changes might need to be made to the stock configuration of your new gun.