I am a bit late commenting as Wednesday is now tomorrow.
It sounds as if you are unsure of your vet's advice? With a Penrose drain it is critical that no infection can get in, and infected pus can drain out. The dilute Hydrogen peroxide will help to keep the drain and wound clear of bacteria. Or you could use "Vetericyn" spray. This should be done daily. With a drain, the danger is always that bacteria can get in, so flushing it is a good idea. I don't see wht dilute Hydrogen peroxide is so bad (?)
Be very careful the drain doesn't 'disappear'. If so, it might have a) been eaten (and that can cause stomach blockage) or b) sunk into the wound if the wound is big enough. That can cause major infection.
Actually, the original Vetericyn product is no longer. The Vetericyn has had the original Microcyn Technology removed from their product and a less expensive HOCl active has been substituted. The original Microcyn Technology is still available in a new MicrocynAH animal healthcare line of products that cost 1/3 less than Vetericyn and have the original Vetericyn formulation with improvements. Longer shelf life and doesn't sting the animal. See www.microcynah.com/video