I haven't used the Sensor Gel Stick, but the photographer running a workshop I took also felt that they were the easiest and safest way to clean the sensor............
I had a DIFFERENT problem... One day, the D810 started getting a fuzzy line near the corner of one edge - naturally the TOP edge so it showed in shots with the sky where I couldn't ignore it. And, of course, once I SAW it I couldn't STOP seeing it!
Used the camera to clean the sensor, still there. FINALLY, back at home, I opened it up, and used a magnifier to look at the sensor... I had a MINUTE hair or length of fuzz of some sort that was sticking out in front of the sensor. It wasn't ON the sensor. I tried to get it out with the rocket blower, and gentle persuasion, and finally VERY VERY gingerly took a pair of tweezers, reached in and grabbed it. It was stuck between two metal pieces (shutter perhaps?) and I had to give it a tug to get it out, but out it came. No more fuzzy thing on the edges of my images although I had visions of hitting the sensor with the plastic tweezers and having to send the body back to Nikon for a new sensor...