The best way to shed and shred is cardio, as others have stated, along with a lower-carb (never no-carb) diet. Plus, cardio floods your system with endorphins and makes you feel positive and cheery.
Swimming is excellent for weight loss, especially in a natural water body. I used to swim a lot in a pool, until I read how chlorine wreaks havoc on your skin, hair, lungs, and testicles.
I do jump rope (20 minutes with a HIIT element) and the elliptical. Both are excellent, low-impact cardio exercises. I haven't been jogging in years. I save my knees and ankles for hiking.
The myth is that you need to do an hour of cardio per session. You don't, and it actually hits your testosterone levels if you are too deep into a caloric deficit. If you keep the intensity high or HIIT, you only need 10-20 minutes to burn fat and chisel up.
I think canned tuna is pretty bleh. I eat tuna sandwiches on Friday sometimes (it's a Catholic thing) but I don't choose it over other deli options if I can help it. Plus, as you mentioned, you are flirting with high mercury if you eat it more than 2-3 times per week.