Solodin

Not in-game, no. The cutscenes are configured to pull your current in-game character setup (as you know) so I'm guessing that's why there's not a "view cutscene" function. It seems like something they could have added to the game, though. Just have the characters load in with their default equipment. Or go a step further and let us choose the equipment the characters have then view of the cutscenes. One can dream~

I have a very simple swap mod request for Tifa. Would someone be able to quickly give the option to place the Mythril Claws over the Metal Knuckles? I love the look of the Mythril Claws but I'm not planning on building Tifa as a caster.

I'm having this exact same issue. No mods at all and being enabled when playing the game.