Is it safe for me to use an oxygen deprivation mask?
Those masks don't deprive you of oxygen - every breath you take through the mask has the same amount as breaths without it. All they do is make it harder to suck in air. Your conditioning issues aren't related to your ability to suck air into your lungs, using a device to make your sucking stronger isn't going to make you breathe easier. Your conditioning issues sound like they stem from too little specific exercise. Fitness has a great deal of specificity. IF you really have a 45 bpm resting heart rate, your cardio is as good as it is going to get. You need to do more work that is representative of what your body experiences while wrestling - conditioning drills that have you working anaerobically. Hill sprints, pushups, pull ups, squat thrusts, this sort of things used in combination, where you're continuously moving and applying your strength instead of just working your aerobic system with things like jogging.
........I don't understand why you want to use something that deprives you of oxygen. I really can't see how that helps increase your stamina. If you want to increase your stamina, do the tried and true: Go running with a truck tire tied to your back so it drags on the ground. Wrap chains around your barbells in certain lifting exercises (e.g. bench press). Wrap weights onto your wrists during boxing sessions. The goal in increasing your stamina is to place even more resistance than what you have during workouts. A dragging, resisting force. Other examples can be found in Crossfit training. That's basically what Crossfit is all about, compared to regular fitness.
Why not just sprint instead of using an oxygen deprivation mask? The safety of it really depends on the person. I can't reasonably tell you it's safe, but some athletes do use them. Depriving yourself of oxygen can cause brain damage among other things. You need to be careful.