The best travel dress shirt I've ever seen, hands down, is the Nordstrom
SmartCare Button-down Dress Shirt (this link was not working properly when I wrote this message, but this shirt has been available for quite some time so I'm assuming this is a temporary web glitch--if I'm wrong, just do a search on the Nordstrom site using the term above).
I bought my first shirt in mid-August last year before a trip to Scotland. I wear this shirt three or four times per month, I've washed it numerous times since then, and the shirt still looks great. There's a permanent crease atop the sleeve of the shirt that appears the same as the day I bought it, and not only is the shirt wrinkle free, requiring no ironing for normal use, but with a very light ironing touch up, it looks as if it has just come starched from the dry cleaners. I pack the shirt in a 15-inch folder for travel, and it loses the creases from the folds with a quick shake and then a hanging in the bathroom during a shower.
During the upcoming Half-Yearly Sale, this shirt is a relative bargain at $32.90. I paid the full freight of $49.50 before my trip last year, and I'd do it again. The money saved in dry cleaning while maintaining an absolutely first-class appearance more than makes up for the extra money you might spend in buying the shirt.