'not as horrible as it might sound'
might indicate that it could sound horrible. However,
might is "milder" if you like.
Might says that it could, possibly sound horrible to the reader.
May says that is will, possibly, sound horrible to the reader.
In the end it is just a matter of using one word or the other, because they both, in this case, have pretty much the same meaning.
It has different meanings in different contexts:
"I might go to the movies.", indicates that I probably not end up going,
"I may go to the movies.", indicates that I actually will end up going.
I hope that is the kind of explanation you are after. Because, there's really not much more to it in this case.