Definitely one of my favorite sports that presents an opportunity to peel off your shirt is bouldering. It's an intense, full-body exercise and it's a lot of fun. Plus, it's a great chance to get outside and enjoy some sunshine and the beauty of nature as many bouldering locations are outdoors in nature. Basically, bouldering is climbing lower rocks without ropes. A crash pad is frequently used for safety to break your fall if you slip. It is always a good idea to have a partner to spot you. He can move the pad to make sure it is still under you if you climb to the side, or catch you when you hit the pad, so you don't roll off to the side and hit something hard anyway.
It's pretty common and widely accepted for guys to go climbing shirtless, especially when it is warm outdoors.
It's even fairly common for guys to shed their shirts when bouldering at indoor facilities and dedicated bouldering gyms.
I highly recommend you give bouldering a try. Find some guys in your area who have the right equipment and ask if you can tag along, or find a gym and give it a try. Be safe, use common sense and proper safety practices. If you like it, you may want to invest in your own climbing shoes and crash pad. So get out there and have fun!