Fishy problem- which stat is appropriate? t-test or mann whitney

Hello kind stats people,
I'm in a bind! In my PhD I'm studying fertilisation success of 2 species of fish when they mate with each other.
So how does mating success as a hybrid compare to that of the pure male. And just to complicate things I have them mating in different orders to see if mating first can increase fertilisation success of hybrid males.

The problem I have is that my data is proportion data- the proportion of eggs fertilised by each male.
I want to compare the success (proportion of eggs fertilised) of hybrid males when he is first to that of the pure male who mates second and then the reciprocal (hybrid second to mate, pure first)- this would be two seperate independent samples t test if I had a continuous variable.

Is it OK to use mann whitney U on proportion data?? Or do I have to arcsine transform my proportions. when I do mann whiteny U I have strong significance (p=0.01) when I do a t test on arcsine transformed I have 0.06, which I am assuming is due to single outlier.

Any help or advice would be greatly appreciated.