A lawnmower blenny should not be in with seahorses. Just because you haven't seen any aggression doesn't mean it isn't or can't happen. Just being there is enough to stress some seahorses enough that they don't remain healthy.
However, assuming the problem isn't due to something like a bite from the blenny, it is probably then going to be a bacterial infestation like vibriosis.
It's not too often that the problem starts at the snout that I've seen. It is possible to have something due to parasites as well in that it isn't in a species only tank.
I just checked in the "Working Notes - A guide to seahorse diseases" and for something like vibriosis treatment is a combination of the lowered temperature, slowly to at least 79° plux medications like kanamycin,gentamycin, neomycin and Bactrim as well as treatment with a sulpha drug.
It must be done in a hospital tank and water quality is maintained by very frequent water changes with WELL aerated saltwater.
Nutrition is important so try to get some live food and gut load especially with Beta Glucan and vitamins.
The best I've found for this is Dan's Feed from Seahorse Source.
ENRICHMENTS from SEAHORSE SOURCE
However, if it is a parasitic problem you have to basically identify what the parasite is to know how to treat it.
Most treatments I've come across for a lot of the common parasites use praziquantel, while some use formalin and others use a dewormer like fenbendazole. Also, with the wound, secondary problems of infection may have to be treated with antibiotics.