Thank you for your question. Unfortunately it would have helped if you
provided additional information because there is honestly a big difference between a 60 year old, 5'2" 300 pound
says they have loose skin in the triceps area, versus a 30 year old, 5'2" 100
pound person with the same issue.
But to answer your question as best as I can with the limited information
at hand, I think it is best if you understand the differences between loose
saggy skin and body fat. As you will see, it is not uncommon for both to be
Loose Skin Vs. Body Fat
If you look at the diagram above, you can see that for most of our
body, exceptions being the palms of our hands and our eyelids, our skin (dermis &
epidermis) is only around 1mm thick.
If you pinch as much skin as you can from your triceps area and it is more
than 2mm thick (1mm + 1mm of skin) the rest is subcutaneous fat (sub = beneath,
cutaneous = skin, beneath skin).
Your subcutaneous fat storage capacity is limitless. In the example
diagram (right) the sub cutaneous fat is small but is several times larger in
most areas of our body.
Most People who think they Have Loose Skin, really need to Lose Body Fat
is good news for you in your case if your body fat percentage is causing your
triceps to appear flabby or not firm.
Weight training exercises which your arthritis is preventing you from doing
provide little or no benefit for losing body fat.
Body fat loss is accomplished by cardio and full body weight training, a
healthy diet, and proper rest. It may not sound right, but for at least
75% of people, lunges, squats, and cardio provide far more benefits for
combating the loose skin in a woman's triceps area because they will help
increase metabolism and help burn body fat significantly.
If you do not have excess fat in your triceps area and there is loose skin,
you can perform any exercise for your upper body which use the triceps as
synergists such as push-ups, chest press and shoulder press. They should
be less irritating for your arthritis.
Another idea if you really want to perform triceps exercises is to get wrist/ankle straps. You can attach them to cables at the
gym and put them around your wrists or forearms and perform the triceps
exercises without involving your wrists, fingers or hands.
Always perform exercises within your envelope of function, aka if it hurts...
don't do it.