Actually, most players will be more likely to hurt the UCL throwing a lighter ball such as a tennis ball, simply because they can get the arm moving faster as they transition from external to internal rotation and thereby put more load on the UCL. The heavier ball tends to slow the arm down and the dynamic load is less.
If a player has enough arm strength to throw the heavier ball just as fast or almost as fast as the lighter ball then the load on the UCL will be larger, otherwise the light ball is more dangerous.
Overload training tends to be less dangerous than underload training when it comes to throwing a baseball, although that takes into consideration more than the UCL. When the arm gets moving faster with the lighter ball the arm has to be decelerated from a higher velocity and the ball is gone so the ball weight has no impact at that point. Underload training tends to be more beneficial for most when it comes to gaining velocity. Risk / reward.
Probably the most risky thing to do, with no discernable added value relative to throwing an overweight ball, is to use one of those weighted gloves while throwing as the weight is still there during the deceleration phase.
The underweight issue is why people tend to worry about the towel drill but I can't see anyone putting as much effort into the towel drill as they do into actually throwing a pitch and it becomes very difficult to achieve full external rotation without some weight in the hand. That's why I say you'd have to be trying to hurt yourself to damage the UCL while doing the towel drill. There is probably some hyperextension danger while doing the towel drill if done too aggressively especially if the player tries to make the towel "pop".