The instructions in the picture are from the Service Manual for a 1997 150HP, but I would guess the instructions for your 115 are similar. The part number is for a Flushing Attachment (muffs) for a 135-225 HP, so the proper ones for your 115 are probably a different size and part number.
Personally, I think I would use the flush port vs. flushing attachment since you have to run the motor at up to 2500 RPM for 3 to 5 minutes to thoroughly flush it. I'd be more worried about not providing enough water to properly cool the motor.
When using the flushing port (motor not running) and normal house water line pressure, water might not be able to get past a new impeller. I would imagine if the impeller has any wear at all, it will allow some water to get past and exit out the intake area. You could have sucked a small amount of sand into the water inlet since the last flush, causing some wear on the rubber impeller vanes. Even normal wear will eventually wear out the impeller vanes and allow more and more water to get past the impeller and out the water intake port.
Mercury says under normal conditions you should change your impeller every 300 hours or 3 years, whichever comes first. If regularly run in shallow water or you beach your boat. You increase the likelihood of sucking in fine sand which will degrade the impeller's performance and life. Fresh water boaters who run in shallow dirty water can suck up sand and gravel just as easily.