The only real list is:
-not pointed (unless rubber tipped)
Round nose have been used in tube mags for around 150 years. Even if you do use pointed, the odds of a magazine detonation are fairly small. It is possible, and a risk I personally avoid taking, but it isn't something that automatically happens.
Some guys only use flat nose or hollow point with a meplat larger than the primer but at the same time the rounds aren't always perfectly lined up (that's why pointed bullets don't cause an automatic detonation). The edge of a flat nose could still end up against a primer. It takes something fairly pointy to set off a primer with the kind of ultra light strike that results from recoil. If you're paranoid, avoiding primers with really soft cups (Federal) will probably do more than anything else.
Because of the chance of rounds like 38 special, 357 mag, 44 special, 44 mag, 45 colt, and others being used in lever guns, most manufacturers don't use bullets that could be an issue in a tube mag. For liability reasons they only use fairly blunt round noses, hollow points, and flat nose bullets. Factory bullets are also fairly soft lead so the tip is likely to deform against the base of a bullet. If they were hardcast with a fairly sharp round nose profile I might have a second thought, but factory soft lead blunt round noses I wouldn't bother caring.
The cowboy bullets you bought, I can pretty much guarantee, were meant to be used in both revolvers and lever guns interchangeably.
If you watch the Hornady videos of testing the rubber tipped FTX bullets they put nylon disks around the cases to get them to line up bullet-to-primer. If they are just sitting in a tube, because they are all rimmed cases, the tip tends to fall to one side so it rests against the outer edge of the case head in front of it. It can line up, which can cause detonations, but it isn't super common. Not using pointed bullets is kind of like wearing a seatbelt. I don't plan on getting into a car accident, but if I do I prefer to have the seatbelt on. Not wearing a seatbelt wont automatically cause a car accident, and using pointed bullets wont automatically cause a detonation.