Wet-cleaning a sensor is commonly done and usually works, but it is not risk-free. The main cautions from users are:

• Be especially careful with cameras that have self-cleaning sensor systems; the filter assembly may be less well supported, so too much pressure is a real risk.
• The biggest practical issue is often not damage, but residue or streaking from using too much fluid.

If you do it yourself, use very light pressure and only a tiny amount of cleaning fluid—typically a drop or two on the swab. Make as few passes as possible. After cleaning, check for residue by shooting an evenly lit plain surface, out of focus, and inspecting the frame for streaks or remaining spots.

Done carefully, residue usually won’t be worse than dust and can often be avoided, but poor technique can make things look worse until you clean again. If you’re uncomfortable with the risk, a camera repair shop can clean it for you. If the spots are minor, you can also postpone cleaning and retouch them in post-processing.