Keep in mind, you can never out work a bad diet. First impotence of cutting is your diet, next is cardio.
The number of days you train is going to be contingent on a couple factors... workout style, and amount of cardio. Everyone is different, some guys will advocate 3 days per week, while others will workout 6 days. I personally do 3 days on, one day off, repeat. IMO, If you are running every day (not walk/run), I say keep it to 20 min. max. If you do every other day, 30 max. This will help you over the long haul.
As LeanEngineer pointed out, even if you are not lifting, you should have "active rest days." Basically, that means you move, take a hike, go biking, cut the grass.... What does your current workout plan look like?