What a nice gift!
I think it would be very possible to get a custom sized latex mattress. They are often made to order (meaning as needed) anyway. We just bought one and opted for an in stock item, but they had lots of options that we'd have to wait a few weeks for it to be made....I'd definitely check into getting a custom size.
Otherwise, if you go conventional (due to cost issues, time line, whatever) let it air out in a garage or out in the sunshine if are lucky to have some.
We just bought this awesome latex, wool topped, organic cotton wrapped mattress and it didn't offgass AT ALL (of course) but our last mattress was a Tempurpedic, and besides the great comfort (yes, it felt nice!) it made us have headaches to even walk in the room with it for at least a week! It DID pass, though i am sure it continued to offgass, so if that is the route you need to go just avoid contact for a week or two if you can.
And really, at least explore the other options. We found a local company that was willing to price things very competitively and even do a delivery even though we just moved over an hour out of the city (with a ferry ride to boot!).