Relax, if you have only just started you will train stamina into the muscles you are using as your shooting continues. Going to a lighter gun can bring its own set of problems.
A little bit of fitness training might help. I found light dumbbells of say the typical plastic ladies trainer sets of 4.5kg Perfect. Go for curls but with the hand over the top of the grip to build stamina and strength into shoulder and Tricep. You wont build bulk (which will be very detrimental) with such light weights. Even so, this weight build up still 3 times heavier than most pistols.
Light pistols bring greater problems in my experience.