As a Green Battle-Eye player, I would say that you need to consider two things:
Do you play on a Yellow BE world? If you play on a Yellow world, then the answer is YES. Use it to get a guaranteed Midnight Panther. As for other mounts, they are not hard to find, so you can use their normal mount item to tame them. But I've lost like 3 Midnight Panthers trying to tame them, because on my Green BE world, I don't have Music Box as an option, and they are not easy to find because you have competition and need to check often, so on Yellow worlds the Music Box is not that rare.. everyone who has a Chayenne Key can make new characters and use it to get a lot of Music Boxes. If you have one and ever find a Midnight Panther, then use it to get the mount as you can easily buy another Music Box for decoration later.
Draptor has a announced raid every week, you should not have so much difficulty on trying to tame them with their normal item, which is not that expensive.
Dragonling you need to find the active Fury Gate and they are always there, Decorative Ribbon like the other answer said, depends if there is a team doing Warzone everyday on your World, but on Yellow worlds usually has some available. Unfortunately on Green Worlds not everyone does Warzones.
Do you play on a Green BE world? Then the answer is NO. Why? Chayenne's Key doesn't exist on Green BE worlds, so the Music Box can only be obtained by contests. In this case, you should only keep it as decoration, since it is very rare.