You can put any type of swag in your geocache.
If you do mention the items in the cache description just note that they are swag items for the finders. The key thing to keep in mind is that anyone might visit your cache so the listing page cannot solicit or have an agenda, that doesn't apply to the swag, just to the cache and listing page. Stick to a description of the cache hunt, tell a story, entertain or educate, just don't solicit, for money or adherents.
Your choice for swag is limitless but you could use your sig item as well. You could laminate and leave small cards that said you were active in supporting that charity as a sig item when finding caches, sig items can be whatever you choose, some people leave business cards and some leave tracts, it is up to each individual geocacher.
As a cache owner you have to create a cache that doesn't have an agenda (beyond geocaching). If you think you have an idea that might work you could bounce it off your reviewer, they can make exceptions but leniency is rarely granted.
Your swag idea sounds like it would support a good cause, perhaps hiding your cache near an off leash area would increase your chances of getting people who might help.
Your idea as it stands is fine, you can do that.
Thanks! I just didn't want to step on any toes right off the bat! Very excited about placing my 1st Cache!
