Take a look at this novel cat product. I like it. It allows a cat to rub his/her cheek against a comb. You put catnip inside it to attract the cat. Cats love to rub their cheek against things because it transfers their scent and we know how to stroke our cats. It often includes stroking across the side of their face and under their chin. This does the job. The cat can do it for herself. The only downside is that it is fixed to the wall with a sticky pad. When the device is removed it will remove some of the wall or leave behind a gluey mass that can’t be removed!
Note: I am not promoting this item on the basis that I get commission or something like that. I just bumped into it on Facebook and liked it and thought other people might also like it and therefore consider buying it. I will certainly consider buying it myself.