Wow, lucky you, you must have REALLY white eyes!
But in answer to your question - no, not all monthly disposables have a handling tint. I can't think of the ones that don't right off the top of my head, but there is a directory of contact lenses that your optician will have (every practice should have one) that will tell him/her which ones do or don't. You should really ask your own optician to reccommend something else if it bothers you, since if I just told you a brand name they might not be suitable for you - everyone has different requirements for their eye health. Good luck!