As Cream told you before, do it separately.
Make a life insurance, and of course DON'T declare the climbing as your activity. They will cover you ALL the activities in your life (drive a car, go to work, daily activities...)
Then through the mountain federation, make your license for climbing. Here in Catalunya with your license in the mountain federation, it's included an insurance. The cost it's really affordable, depending the activity.
Just for your information:
Federation license class "D" (one of the HIGH license) covering:
High mountain (up to 7000 m.)
Sky in all terrains (nordik, mountain, telemark...)
COVERAGE ALL THE WORLD less polar zones and mountaines +7000 m.
The coverage it's the following:
Dead: 20.000 eur
invalidity: 35.000 eur
and several coverages ( rescue, medical costes, repatriation...)
I don't know where are you from, but ALL countries has his own federation, with similar services...
Hoping that this information will be useful for you...