Can you still enjoy the sun after having one skin cancer removed?

Yes with protection. Sun block, long sleeves, and limiting time exposure to the sun is a "bright" way to avoid a recurrence of a already susceptible epidermis and previous cancer..
Enjoy the warmth. As a mohs surgeon, I see a lot of patients with skin cancer. I tell them to enjoy the warmth of the sun- but not the rays. You can still go outside and enjoy your activities but be sure to cover up with clothing and sunscreen. Having one skin cancer means you have had enough sun in your lifetime to cause one to form. Reducing your sun exposure will help prevent future skin cancer. So cover up.
Yes. Yes you can. But you need to limit your exposure to uv radiation from the sun. Wear sunscreen on exposed areas, and cover up when possible.