Pou doux ( pronounced pudu/ poodoo ), French for "soft louse".. That thing can be infinite.
Frankly, I think that the best you can do here is to go for the least bad and the most probable / likely, according to you, assuming like there was a mistake in the kana initially, or that we're just in front of a wall.. or just keep Pudurare or maybe Rare Pudu.. or go with anything you think is the best. Or wait for others to talk also.
And for me, the thing that rings the most bells is definitely the shy rear. I think that pudu has not to match exactly a word that means shy, for itself to be intended to be meaning shy actually ( I hope I make sense x) I struggle with English sometimes ).
If you end up opening that to votes, I'd definitely go for the timid ass thing.