CM,
You're right - a nuclear-armed F35 shouldn't be any more vulnerable than a non-nuclear-armed one. I'm just concerned that an opponent able to rile you to a nuclear attack is probably able to field an air defense able to deal with an F35 arriving to deliver it.
If the F35 is to fire a stand-off weapon, then would it not just be cheaper and easier to use more conventional and cheaper tools to carry it to the launch point?