Yes, Urad can be used both on alligator and ostrich skins. However, in both cases, there are things to be cautious about.
First, these skins have uneven areas where Urad wax can build up.
Second, these skins sometimes have both a non-porous thin surface layer and a thicker very porous undersurface layer.
The way to avoid possible problems related to these two points is to mix Urad with Tenderly (about half and half) and spread it very thin and very quickly. Because if you spend too long going over one spot, it may wet the porous undersurface of leather too much which can result in your leather becoming darker (noticeable on lighter colored leathers). In short, use Urad and Tenderly mixed together and spread it thin and quickly.
The above is what has worked best, with thousands and thousands of boots of testing! However, we have had one case of pink ostrich cowboy boots where using Urad without Tenderly was what worked best! Exceptions do exist so the above advice does not remove the general rule to always perform a test in a less visible area first.