Get one of the cheap(er) slip on recoil pads and try it, first. And try it with all the loads you are regularly going to use.
This will tell you if the extra length to the stock that the pad adds is of any importance, and it will tell you if you actually need a pad, and how badly, if you do.
THEN look at a generic "cut to fit" permanent pad and if you'd be doing the work yourself or paying a professional. If you're thinking of doing it yourself (whether you shorten the stock, or not) read up on the best way and tools to use, (and why tape is your friend,
). The work is not difficult but the first few attempts rarely result in a professional quality looking fit.
Coach guns often have "short-ish" stocks. This makes them a bit handier and probably comes from the shorter length stocks found on some of the originals when men were, on average a bit smaller. Depending on your personal stature, you may find adding an inch or so with pad might be a desirable thing.
Find out using a slip on pad, and then you'll have a better idea of what you'll want, before doing any permanent work on the gun.
And, do you testing wearing the clothes you'll be wearing when using the gun. Summer t-shirt and winter can coat make more than a bit of difference when it comes to mounting and shooting the gun, too.
