Firstly, you should know that resizing is the most important part of printing. If your lab needs 300ppi, you provide 300ppi. End of story.
Secondly, you're NOT increasing it!!!!!!!! The resolution of the photo (at its full size) is WAAAAAAAAY higher than 300ppi when the size is 17mm wide. Try it and see! In the Image Size dialog, temporarily turn off the "Resample image" checkbox, then change the width to 17mm. You'll see the resolution shoot up to the thousands, probably.