A very common and idiomatic way of using 'possible' in a sentence is to use the construction:
as X as possible.
where X can be any number of adjectives.
as little as possible.
as much as possible.
So, I think, in quoted speech, where informal grammar is acceptable, you could 'quote' the character saying something that English speakers will often do - which is (sort of) making words up on the fly where they are needed.
Come on, hop on my back and try to make this as un-silly as possible, I don't want the girls to see this.
'Un-silly' is a single word adjective which might well be used by someone, although it is not in a dictionary. Just adding 'un' reverses the meaning of the word. 'Un' can be used with other adjectives which [cough] might be used here.
Or avoid the negation, and say it this way:
Come on, hop on my back and try to make this as sensible as possible.
Or reword to avoid the whole problem
Come on, hop on my back, and try not to make it look dumb/stupid/embarassing.
Of your three choices, the first one is the closest to being acceptable, but I would suggest none of them sound entirely natural, and the second two are ungrammatical.