"How about a Kenai chest holster with a handgun in it instead.

A big, noisy handgun. "

As an ambush predator, the victim ordinarily doesn't know there is a cougar around until it's crushing the victim's neck, making a handgun of little use. In this case the cougar behaved strangely, allowing the mountain bikers to notice that the cat was trailing them. A firearm would have been useful this time. Or bear spray; that would have worked also.