Did you ever get your questions answered?
To get his papers, you need to contact the current owner on record (meaning, who the ApHC considers his owner). They need to sign a transfer over to you (technically it would be to the person they sold him to, who would sign it over to the person they sold him to, all the way down to you... but if you can get one direct to you it will work) and give you his papers. If they lost them, not sure what the ApHC, I know with AMHA/R (I forget which it is I had lost papers for when I sold a horse...) I had to sign a form stating they were lost/destroyed and how/why. Yes, if the guy wants to charge for the papers, that is legal, and done often (as was stated, ethical is another story...).
If that doesn't pan out, once gelded, as was mentioned, he can be hardshipped.
A crypt is definitely fertile, as you're aware. But it CAN be passed on, so crypts should NOT be bred. It costs a lot more to geld a crypt as it's a much more invasive surgery. But it SHOULD be done. The retained testicle can become cancerous, among other reasons to geld.
Good luck with everything! I love Apps, would love to see photos :)