The spring after planting, I had a cherry & plum that both leafed out, then the tops died. Sprouts appeared from low on the trunks - above the graft - and I just let them grow to see if they'd last another winter. This spring they leafed out and are looking quite healthy, so I figure it's time to make a decision. The cherry has two branches, both starting very low, just inches above the graft. Do I need to choose one to avoid having it split in half at some point? The plum's lowest shoot looks like it would make a reasonable replacement leader - but I'm chicken to remove ALL the other branches. How bad would it be to start with the other branches, despite them being a bit crowded and low to the ground? Thanks for any advice!
For the cherry I would choose the longer branch and tie it to a tall stake to ensure that it becomes the leader. The other branch can be left on for a while, but any new shoots should be pinched off so that it doesn't get much larger before being pruned off after a year or two. You can do the same thing with the plum, limiting the growth of the surplus low branches and removing them after the new leader has grown tall enough to produce branches at the desired elevation.
The way your trees are branching is not very favorable for splitting. Both the cherry and the plum have branching point for their 2 major branches at different heights, although the height difference is not big. Those trees would be much liklely to split if they branched into two equal branches at one point. Like V. So any method to promote one branch as a leader and suppressing the other will do, and you are not urged to remove the unwanted branch very soon. Suggestions by Vitog should work very well. Because plums and cherries have some problems to cover large stem wounds and those wounds would heal better, if there is a branch nearby, I would not hurry with removing one branch before the wound of the missing top is almost healed. I'd keep the nearest branch to that wound for healing support, and trained the lower one as a new leader.
Whatever you decide to do the best time for pruning is early in spring when the tree is very close to the point of breaking dormancy.