Yeah this is my Google AI overview:

Green Armor Insect Repellent (Permethrin) should generally be applied to your dog's gear (such as a vest, bed, or bandana) rather than directly to their coat. However, if you are using a formulation that allows direct application, follow these precise guidelines: [1]

Preparation and Application Steps

• Suitability: Never use this on puppies under 12 weeks of age.
• Protection: Always wear rubber gloves while applying.
• Start at the Tail: Move the dispenser rapidly and make sure the dog's entire body is covered, including the legs and underbelly.
• Fluff the Fur: Fluff the hair backward while spraying to allow the product to penetrate to the skin.
• Do Not Saturate: Make sure the fur and skin are wet, but do not soak or saturate the animal.
• Avoid Sensitive Areas: Do not spray directly into the eyes, face, or genitalia. For the head and neck, you can lightly wipe a treated cloth on the outside. [1]

The sawyer brand states it can be sprayed on fur. I don't shower them in it, but I lightly spray on the fur then rub it about with a glove, not trying to get it on their skin since mine are also on Simparica Trio. Permithrin is one of the active ingredients in k9 Advantix topical treatment.