I think this would likely be dangerous and counter-productive. The part that could be dangerous is nutrion; it’s important to make sure you’re still getting enough of the right foods. Obviously, if you’re just cutting out beers, sodas, and french fries, you’re probably still getting the same nutrition you were before, but some people take it too far and will try to get by on a couple salads or whatever.
Another thing to consider is that a cut calorie intake is not a linear relationship with weight loss. The starvation mode concept isn’t true, but your metabolism does become more efficient as you cut calories so you get to a point where the extra calories you cut just isn’t worth it. For instance, I believe my base caloric intake is somewhere around 3500 calories. If I cut it down to 3000 calories, I could expect to lose roughly 1 lb a week, but if I cut it down to 2000 calories, I probably would see noticeably less than the expected 3 lbs a week.
In this case, as someone pointed out, he’s eating 2000 calories, from the napkin math I saw up thread, right before bedtime (which is, of course, the worst time to stuff yourself) and probably has at least another 1000-1500 calories in there somewhere. So, I’d be concerned that cutting down to 1000 calories could potentially undernourish the OP.
As others also pointed out, the whole “fat burn vs. cardio” thing isn’t supported by research anymore so, really, it just comes down to how much time you have and how hard you’re willing to go. Do whatever you can maintain for the amount of time you have available. Also, be careful not to overdo it because it’s also easy to burn yourself out before you learn what your limits are.
Finally, I strongly suggest at least SOME weight training, even if it’s just a few rounds on a circuit. A pound of muscle burns more calories over the course of a day than fat, so you don’t just burn the calories from the weight training (which itself is non-trivial), but any muscle mass you gain burns extra calories all day. So, chances are, if you have an hour to work out, you’ll likely see better fat burning results by doing 30 minutes of weight training and 30 minutes of cardio than just 60 minutes of cardio. Moreso, weight training has other benefits including gaining muscle tone, so you’ll also look better faster.