[Thinlizzy]

I think your chances of harvesting a cougar with out dogs is very very slim.
My friend was a teacher in Hinton for a number of years so I spent lots of time driving/hunting the logging roads all around Hinton.
In 5 years of doing that I saw one cougar cross the road in front of us.
I think your best bet would be to save the 2 to 3 grand it costs for a hunt and get an outfitter.
Is it possible to get one with out dogs. I guess anything is possible but your chances would be super super low.
If it was snowing and you cut across a fresh track you could possible track it.
Hopefully that helps. Phone the local fish and wildlife office and they may be able to put you in the right direction.
Hope that helps.