Thanks. I was mainly interested in the technical aspects but I am a diver and know that without the appropriate license, dive shops will not rent or sell you gear/air/whatever. However, if you show up with a pilots license with a high-altitude endorsement, explain the situation to the owner etc. and generally be honest and professional about your intentions, and obviously bring the correct adapters, I'd say there's a fair chance they'll help you anyway.
In fact, what I would do is pay a visit to my local dive shop beforehand, without the bottles and things, and have a chat with the owner about it. See what he thinks about it, set up an agreement about the way it's going to be done.
After all, there is no *legal* requirement for dive shops to check your license. It's just that as a matter of keeping the sport safe, dive shops all over the world have agreed that they will not help customers without checking whether the license someone has is compatible with what they're buying. They will not fill your bottles with air unless you have a basic divers license (PADI OW, for instance), will not fill your bottles with nitrox unless you have a nitrox license etc.
Anyway, the highest I've been to so far in my aviation career is FL55 (and 32 meters in my diving career), so who am I to offer expert advise on this?