It would be funnier if it had fewer verses. It's a one joke song and the joke does not support five verses. I'd keep it down to verses 1,2 & 4.

It doesn't make fun of transvestites. It makes fun of the man who feels uncomfortable when unexpectedly meeting transvestites.

Of course it's in bad taste, and it would not do to sing it in the drawing room to one's maiden aunts. (Equally, of course, it's just the kind of song that those maiden aunts would sing amongst themselves.)