I believe that, as normal practice (and also in your interest), HSWA will rather not send a watch to Geneva if the work can be done locally. However, I would advise you to discuss carefully all possibilities in person and with your watch present, as the options may not be so clear cut, including laser welding. I would just reserve a full case replacement as a last resort, but if you are convinced after you have discussed *together* all other options, it's something that again I don't see why they should oppose. In this case, just keep in mind it WILL be expensive ;-)
Let us know what you decide -- but as I said earlier, I wouldn't totally discard the "simpler" option to wait and get everything done at a later stage, when some issue to the case is more evident and/or you need the watch to be serviced anyway ;-)
Cheers.