If weapon skins remain as individual items, then yes, the stash NEEDS to be increased (I'd hope for at least 75 slots).
If they get lumped into apparel, I don't see the need:
1 PvE gear set (5 weapons, 1 sidearm, 6 gear pieces) 3 pieces total in inventory, equipped gear takes zero space. PvE has yet to show ANY indication that anything but a solid dps build is needed, as healing skills work well enough even at their lowest stats.
4 alternate gear/wep sets at maximum (pvp sets for dps, healer, electronics, hybrid/experimental/tank/etc) assuming a full loadout for each, 48 pieces in inventory
total of 51 pieces in inventory at maximum at any time. If you realize that changing your weapon has very little bearing between builds, we can shorten this to 27 (6 pieces of gear per set, plus 3 alternate wep types). You still need to be able to do SOME dps in any build, even if that's solely from weapon stats. My lowest backpack on any character is 50 slots, so I'm left with 23 empty at the least, if, for whatever reason, I'm carrying every set I'd ever use at once (fat chance). There's zero reason why you couldn't decon items you collect as you go along to always have free space (even the final fight at the UN doesn't hand you 23+ items at once), and you'll NEVER have 23+ items worth saving from any run (and by the time you should be collecting drops, the fight in that area is over, you have all day to play with inventory before moving on). No matter how you try and justify it, there are items worth saving, and then there's the 99% of everything else that's never going to be an improvement, or even worth holding on to.