Its not that big a deal and there will be worse things to deal with on a rtw. If you can't deal with your own snotty hanky, don't go to India for a start. Forget Africa. Probably South America, China and any other undeveloped country. You won't be able to buy tissues in quite a lot of places and one pack of tissues isn't going to last long once a cold takes hold.
Besides hankies are useful for so many other things - round your neck to keep the sun off, over your head for going into certain religious places, on your head to look like the biggest dag from anywhere, to stuff in the end of a pair of new shoes that turn out to be too big, round your neck if you are freezing and you are inadequately clothed, to wash yourself with when you've lost your flannel/washer, to dip in some water and refresh yourself with in any number of situations and so on.
Whereas tissues have one use only and can pass on disease if dropped somewhere where there is inadequate disposal - many places - and making the landscape filthy where therea is no disposal system - which is not that uncommon. Unless you want to try to bury it.