shaking....

A couple of friends have shaking issues.  This is from medical issues, both being  different.  My question is would a smaller length barrel be beneficial?

I would think the opposite.  Think of holding a ten pound block of steel in that hand that is trying to shake.
This assumes the shaking is NOT due to holding a weight.
For me, because of arm strength, the heavier the gun, the more it shakes.
The more the mass, the less it will want to move, but the harder it will be to hold it up.

Do you shoot irons or red dot? If irons then a longer barrel & sight radius would amplify the wobble in your sight picture. If you have a red dot then a longer barrel is going to just change the balance of the pistol.

I was thinking more along the lines of the bullet being in the barrel for a long period of time.

It might leave the barrel a millionth of a second earlier. I doubt you'd see much difference on paper. I would work more on finding a gun that feels good in the hand and helps minimize your wobble.