10 man Malygos is easy to kill solo, and as mentioned by Ideon the Azure drake does drop in this difficulty. The approximate drop rate is 3-4%.
I have done this fight as both retribution paladin and windwalker monk. A rough guide on how to do this would be:
1) Pull the boss and pop your damage cooldowns. If you have cooldowns which allow you to do any extra damage at range then save these.
2) When Malygos lifts off at 50% and begins the phase transition into phase 2 he will be out of range of melee attacks. This is the best time to use any ranged abilities to try and burn off as much HP as possible before he moves out of range entirely. This will make phase 3 much easier.
3) Scions will spawn on small floating platforms. Kill the ones which come down to the ground and jump on their platform, then fly up and finish the rest off.
4) As phase 3 starts you will land on your red drake. Stack up your heal over time just before Malygos becomes targetable (Ability number 3, max 5 stacks) and then start a rotation of fireball x3, fire breath x1, HoT x1 (1 1 1, 2, 3) and repeat this. You should not need to use the shield as long as you always have 5 stacks of the HoT. Just make sure that you move out of the static cloud as soon as you can. On average it will take 15-17 stacks of fire breath on Malygos before he dies.
5) Loot, and hope your mount drops :)