Lower gearing for sure. Nothing to do with fitness, just about tuning your gearing to the ride you’re doing and enabling you to pace yourself better. A 32 out back should be OK with small chainring up front. You don’t need the big gears unless you’re wanting to gun in down hill. You get to scary enough speeds just freewheeling down an Alp, so sacrifice your higher gears by going for smaller chainrings. You’ll have more than enough gearing for the flat since you’re not riding at high speed in the middle of a peloton.
Pacing if very important. I rode Mt Teide with my brother a few months ago. We’re both pretty fit but I’m a good 20kg’s lighter than him. He knows all his training zones and was pacing himself. I was amazed how slow he started out, I usually go out way too fast so could probably improve my performance just by better pacing. I get away with it on my shorter and less hilly rides in the UK, but a 50+ mile ride with over 5k ft of climbing is a different story altogether and the additional 20kg’s was taking it’s toll. In the end he was waiting for a good 45mins at the top for me.
I’m planning following the tour through the Alps with a mate in the summer and taking our bikes to tackle some of the famous climbs, so in training for that. I’ll definitely be putting a 32t cassette on, but I’ll also be making a concerted effort to lose some timber. 10kg’s will transform my climbing pace even at my current fitness levels.