Taking care of your dress shirts seems to be quite simple: you can always carry a practical travel iron or take advantage of the laundry service at hotel where you are staying.
For ties, unfortunately, this is not so simple. Of sensitive material, the silk, the tie has a length that requires to always be folded for transport. And these folds cannot then be leveled with a simple iron, or you may ruin forever your precious ties. What to do then? Is it really possible to iron a tie without an iron?
There is a very effective trick to stretch the fibers of the tie without damaging the fibers of silk and keep it in top shape. Once you arrive at your hotel, hang carefully the ties above the shower or bath, and proceed to open the hot water underneath for about five / ten minutes (maybe take the opportunity to fill the tub for your bath). The water vapor hence generated will penetrate into the fibers and distend them in the same way as a professional cleaning service!
Seeing is believing.