With the existing morph system this likely would be a lot of work. Having a morph active will block you from switching weapons, and this is by design from the original Heretic/Hexen implementation of it.
I take it that this weapon limitation isn't the same sort of list of weapons that a default player uses? I imagine it would be an easier path if treated so, as having a singular weapon in this list (as in the case of heretic/hexen) would behave exactly the same as denying the ability to switch weapons.
That's understandable, even working with it in ZScript feels super hacky. I'd volunteer to figure it out if I was any decent with C++. Is any of the morph code exposed in ZScript? I couldn't find anything poking around.
EDIT: Found some parts of it, but definitely nothing accessible that I can change this behavior and offer it as a pull request. Oh well! I'll take the No on this one, maybe bump it if I ever decided to dig my teeth into the deeper source.