duuuuuuuuuuuuuuuude so what's wrong with fumes?
Once E6000 is fully cured it's water- (and I suspect) drool-proof
It will not dissolve and I doubt that any of the chemicals would cause much harm unless your babe would chew on nothing but dried E6000 LOLOL which I doubt she does!
And if you work quickly the hotglue will smooth okay - and you will get used to the temps melting your fingertips (or is it "you'll get used to losing all feeling in the tips of your burned fingers" ? lol)