Marill is likely your best bet. They’re small and light, and above all else, many of them have a special ability that allows them to resist the cold. Moreover, even if yours evolves, it won’t get that much bigger, so you won’t even need an everstone. The line is also fairly easy-going (and thus can be trained for heights), and their sensitive hearing is a bonus for detecting mechanical problems. Just be sure to ask specifically for a marill with Thick Fat, and you’ll be fine.
Other than that, there are the standard flying-types, such as (and especially) the partially ice delibird. However, keep in mind that some of these evolve, so you may need an everstone to keep them at the right size. Additionally, be careful and don’t let them take flight while you’re in the air unless you’ve trained it to give you a warning when you do (and to not open the doors or mid-flight). Certain ice-types such as cubchoo or fighting-types such as the machop line may also work so long as you give them an everstone—the former because of their ability to withstand the cold and the latter due to their bravery.
Just about the only types I wouldn’t recommend are psychic-types (whose powers may interfere with your instruments), fire-types (unless you can train them to control their abilities), electric-types (same), rock-types (due to weight), or steel-types (except for mawile and lucario—also due to weight). Some poison-types might not be a great idea unless you can control their fumes, and while ghost-types aren’t actually dangerous, they’re generally seen as bad omens, so keep that in mind if you’re ever hired by someone else to fly.