The Indus

Can be paddled all the way down to Kargil and onwards (not advisable because of the Situation in Kashmir) and on some hair rising rapids down onto the Pakistani plains (even less advisable due to the situation in there).

Anyway, the Indus offers some good class IV water all the way to Upshi from the starting point in....just drive up until the army stops u where the restricted area starts. After Upshi the river is mainly Grade II (one overhead dam which is best carried, even while some flows might allow to run it) all the way past Leh to Kargil where then some Grade IV rapids will await you.

The others in Ladakh....

There are some rivers in the Nubra Valley which are basically meandering, quite Grade II-III rivers. The rivers joining the Zanskar from the Zanskar Mountain Range are some raging powerful creeks with some freezing temperatures...Many of them continuous but maybe worthwhile a consideration for a group of Expert Paddlers....