If everybody thought he kept the wand then he would lose its mastery at the very first bar brawl he comes upon. Everyone would want a chance to disarm him, and no matter which wand they took off him they'd take the mastery too.
Of course you can. Lockhart ended up the way he did because that was how strong he intended his Obliviation of the boys to be. But we see the spell being used to lesser effect (Hermione's use on Rowle and Dolohov) so I can't see why one couldn't do that to oneself. In any case, one can implant a false memory like Tom does to Morfin and Hokey, or as Lynn proposed, have someone else hide it without telling where it went and modify that person's memory.
Of course you can. Lockhart ended up the way he did because that was how strong he intended his Obliviation of the boys to be. But we see the spell being used to lesser effect (Hermione's use on Rowle and Dolohov) so I can't see why one couldn't do that to oneself. In any case, one can implant a false memory like Tom does to Morfin and Hokey, or as Lynn proposed, have someone else hide it without telling where it went and modify that person's memory.