I think dream was referring to the $42 unit.
If you can get the relay in a timely fashion I'd say go for it, but if it were me, well ... a starter relay is a starter relay -- they all function in exactly the same way, with a coil and heavy contacts. Frankly, without knowing who made the relay and their history I always go with the proven most reliable components possible (Drum roll, please) ... Honda! Bet you didn't see that one coming, did you?
Well, that is if you are sure the relay is bad. As if you haven't already, check the signal leads for power (when the starter button is pushed) and ground, probably through a side stand switch.
The only problem is the differing signal connectors, and Mike, I know you can deal with the wiring end of things. I would recommend finding a compatible connector that can be cut from a damaged wiring harness to ease connecting things up by making a jumper plug using the original plug and the salvaged one. In this way, either the Honda or the Aprilia relay will plug right in. The most fun is getting it securely mounted, but I'm willing to bet it wouldn't take much effort. There is a fly in the ointment, however -- list price for the relay for a 919 is $70 (!) Calm yourself. Go to a salvage or check EBAY: one of the toughest parts on a Honda is the starter relay, so pick one that looks either similar in mounting or for ease of adapting, such as the Honda unit's rubber cover with a provision for mounting on a sheetmetal barb bolted to the frame, and hook that puppy up!
Incidentally, I've heard the Aprilia voltage regulator can be replaced with a Honda unit as well. Worth remembering.
If it has already been done, it is safe to assume it is possible to do it.
On the other hand, if it has not been done never assume it is impossible to do it.
------- Rob --------
BTW I already checked the relay; it clicks when the starter button is pushed, but did not get 12v out to the starter. The bike starts right up when relay is bypassed. Also the wire going to the starter was a little loose on the relay post. Not sure if that caused the relay to go out.