Removing obviously dead wood, even when it's a large branch, won't harm this or any other tree. Quite the opposite is true. Leaving dead branches is an invitation for insect and fungal problems. It can be pruned out now. Before cutting, check one of the many online sources for the proper way to do this for a large branch. It is important to cut cloise to the trunk, but you also need to leave enough of a branch collar to promote rapid healing.

dont know where you are ... but a bad winter can cause flower failure .. and even sporadically on one tree ...

you better wait until the tree leafs out.. to confirm its a dead part ...

proper pruning never killed a tree ... leaving dead stuff can .. by not letting the tree heal over the cut ... and allowing internal rotting ... suck it up and just do it.. if and when the time comes ...

with a better pic of the area to be cut .. we could offer guidance..

but honestly... i cant figure out the pic.. and how high up the red mark is ... it almost looks like its third story????

ken