They should be able to print psd files. Otherwise they are not worth bothering with IMO, as it is one of the most common formats used at least among professionals.
Print shops have to deal with that kind of thing all the time, because they print for businesses and such, and a lot of image formats don't actually specify how big the image should be printed (basically the only reason the dpi setting exists)
PSD specifies that, and also specifies what color formats should be used, as well as transparency (not that the latter matters much if your image has a white background), and when printing at home I find it gives good results, and better than some other programs.
Alternatively, converting it to PDF should work. PDF also has the ability to print to a certain size (probably one reason why it's so popular), however the actual size will sometimes depend on the printer you're using, because printers have a certain margin and they can't print outside that. That's easily solved by using a larger printer if you're a print shop, but for us at home stuck with A4 it's not that easy.
I worked at a print store for a while. A lot of what they printed was just in black and white but they did also do color, and more importantly they did custom jobs where they helped design a poster and so on. Their computers all had Photoshop installed. Maybe it's different where you live though.
