I'm in a suite in just over a week. If you hold on to both boarding passes "to make sure he doesn't lose his," you should be fine.
The BP has priority in red on the top left, but like you said you could pass that off as FTTF. The only spot on the BP that gives it away is on the top right-hand side, under a bar code, is your VIFP number in small type, and under that it says "Category: Suite" with Suite in Bold. But it's in a 10 or 12-point font. It doesn't really stand out unless you're looking for it.
Can confirm what others said, your luggage tag will say Priority, but it won't say Suite