Spot on's take about 24 hours to completely dry, but as long as you avoid the dosing spot, you can touch your kitty as often as you like, no waiting. Keep pet inside, also, for 24 hours to prevent exposure to rain or rolling in dust.
If you use a syringe (without the needle, of course) you will be able to get the dose down through the fur easier. Use a 1ml size. The vials the factory uses are kind of klunky. Just avoid the site where you put the dose on for 24 hours, if you can.
I looked on the web to research the cat's Revolution worm medicine and this was frustrating. I suspected my family had a misconception about the medicine and we all had been not touching her for five days.
The only ill effect I could find in my research was about rashes and hives.
Lately, the cat has been sequestered outside most of the time because one family member is convinced that the medicine will contaminate the furniture (which I really doubt) and I have been insistent that she can come inside.
The revolution is harmless to people as long as they don't drink it. It will not contaminate furniture either. Millions of people use these products every day, even houses with small children in them. There is no danger.
Spot-on treatments usually have an alcohol base and that can damage some finishes on wood furniture. However they rapidly dry enough that that would be very unlikely to happen. Note it's a different alcohol to that in our drinks.