In reply to mortirolo:
As others have said, it depends. What do you mean, ‘climb the Dolomites or the alps’?
if you mean, ascend some of the easier high peaks by their standard routes, then lack of arm strength won’t be an issue. Most will involve long periods of walking or easy scrambling, where your fitness will stand you in good stead.
The biggest challenge will be the mountain skills to safely operate in that environment- glacier travel, avalanche awareness, reading the weather, route finding. And dealing with the exposure; in my very limited alpine experience, I found the need to maintain a high level of concentration due to crossing terrain where a slip would likely be very serious, for hours at a time, very hard work mentally, and very different from anything I’d come across in the U.K., or Pyrenees.
I’d agree with others who suggested hiring a guide; or, sign up for an alpine skills course. That will get you into the mountains, without having to build up the mountaineering skills first, and you can decide if it’s something you then want to invest the time and money to get competent at.