I rode up Ventoux last month from Bedoin. The steepest sections were about 11-12%, but there were a lot of them and they were long. The other challenge is that it can get extremely windy at the top so even though you're going slowly, the non-aero position on a MTB could be a factor.

I would suggest leaving both bikes at home and renting a road bike instead. Shipping bikes is expensive (~$700 per bike each way) and you'll have to deal with the logistics of dealing with a bike when you're there. You could bring it with you on the plane. That will be cheaper, but the logisticial hassle will be greater.

There's a large LBS in Bedoin and they have a small warehouse of bikes. We ended up renting Madone 4.5s for about 40 euros a day. The best thing is that they come with triples and 11-28 cassettes.

Ventoux is truly epic, but the riding around Alpe d'Huez was far more scenic and inspiring. We rented bikes at the foot of AdH in a town called Bourg d'Oisans.