The sensor is protected by a filter in front of it. So you don't actually touch the "sensor" itself. It's not that fragile... just don't rough it up so much that if there's anything that you could scratch you end up dragging the abrasive offending bit all over the filter and scratching it.
I go through progressions to clean my sensors.
(1) easiest is to just remote the lens, point the camera at the ground, then force a self-cleaning. If there's a bit of dust on it then it may just fall off and out of the camera body.
(2) I hand blower (rubber bulb) can give a few puffs of air and that'll usually clear the sensor if the self-cleaning cycle didn't work. Avoid cans of compressed air. If can spit fluid. Also if you blast too much air the rapidly decompressing gas has a freezing effect and that can just attract water condensation ... then you get water spots.
(3) if that doesn't work I have a very soft brush and a few gentle swipes might just take off the offending bits of dirt.
(4) if that doesn't work I INSPECT the sensor using a magnifier to see what's on the sensor that won't just fall off, won't blow off, and won't swipe off with a soft brush. I have a LensPen sensor cleaning and I also have Eclipse cleaning solution and PecPads or SensorSwabs (a few drops of Eclipse on the swaps or pads and a gentle swipe across the surface will generally do a perfect job cleaning it.
When swapping lenses, tilt the camera downward to avoid debris falling into the sensor body.