It would be possible to set up a way to either move or alter a hard point, unless skins are set up to recognize the change in weapons. The possibility comes via having the 'Mech be down for a long time while the change is made (say, 2-3 missions). It can also be set up to require specific (and difficult/rare to obtain) resources to even consider having the chance to make the adjustment, then add on a Tech/Engineer/Scientist who can manage the work and/or a workshop that can handle such a modification. It can even be specific to the weapon mount desired, such as a missile mount for above-mentioned Hatchetman, and you'll only get several, over all, in the entire campaign.
Where Omnimechs gain is that you don't need the mounts, per se, as they come with the Clan Weapons (kind of like CASE for their ammo), your standard repair bay can handle the conversion, and it would only be out of rotation for a single mission for the change. Alternatively, instead of having specific mount types, they just have Weapon Mounts that anything can connect to, ala MechWarrior 4.