Kodiak,

Same as Hammerdown, I put thumb tacks about 1/2" long between the felt layers so they can't be seen. I used quite a few of them to hold the felt from sagging.


[Linked Image from i.imgur.com]


To be on the safe side though, I used a few small finish nails with flat heads, about an inch long, on the legs and base of neck to secure the hide against the wall. The hair hides the nails unless you pull it back, like I did below. I know you said you didn't want to put a hole in the hide, but a few small nails does hold the hide very secure to the wall and are easily hidden in the hair.


[Linked Image from i.imgur.com]