Maybe a week or two at a guess. If you do dry it without salt it needs to be kept in a dry place, even when dried or it'll go moldy but if kept dry it'll be fine.
Sheep skins, deer skins etc. the same. Try to remove fleshy and bloody bits off the back by scraping carefully with the back of a knife. I once had a sheepskin as a bedside rug for over a year before a mates dog ate it while we were at the pub.
If you want to get it tanned don't salt it.
If you want to try curing it yourself https://www.youtube.com/results?search_query=Skillkult+tanning+skins