Can excess skin on the tip of my right thumb be removed? (Photo)

I wouldn't recommend skin removal as the sensation at the tips of the fingers are very important for tactile sensation and scar never has as good of sensation as natural skin. You don't say how long ago your injury was, but if it has been less than a year, you likely still have some swelling.  The size of your thumb may not change though if the bone was fractured, which is a distinct possibility given that the entire distal thumb looks larger.  Give it time, then decide.  Good luck.

Post-traumatic change in shape of your thumb is more likely due to undiagnosed fracture of the sub-ungual distal phalanx than to "extra skin."Smashing of your thumb crushed and flattened the bone, avulsed the nail plate, and flattened the overlying nail bed.  The new nail plate grew in, conforming to the flattened nail bed shape.  The evidence is that from end-on view ( not shown here), your un-injured thumb tip is not as flat as the injured one.  You don't have extra skin, but the skin you have is distributed differently due to the changed shape of underlying skeletal support, and perhaps scar tissue as well.

and more appreciate the larger size of the thumb.  This really can't be reduced in a reliable and safe manner and its best, as someone else suggested, that you enjoy regular manicures and you may find that your thumb slowly returns close to your pre-injury size.