How Long do Warts Live on inanimate objects

I have flat warts all over my body....more warts than there are people in china as my doctor says.  I've had them for about 10 years and they do not go away with any treatment.  So far my 8 year old child has not caught them from me.  But, tonight, he saw my razor and started to pretend to shave with it.  I use it to shave my legs and armpits so I'm sure it is a good way to spread the virus.  My son cut his face with it.  I have not used the razor in 2 weeks and when I use it I rinse it off briefly with water.  Could the wart virus still be living on that razor and be spread to him?  I was so scared I made him hold apple cider vinegar on the cut (ouch) to try to kill the virus that he might have caught.  What are the chances he could catch my horrible ugly skin disease this way?