Most carriers of the HPV and genital herpes viruses have no idea that they are infected, yet they are (to some degree) capable of spreading the disease to others.
There is no way for a man to test his HPV status in the absence of actual warts. Anyway, most people have HPV infections of some sort at some time in their lives, and most of those infections clear themselves.
Herpes is usually diagnosed from testing the fluid in the lesion, but can also be diagnosed by blood test.
About "burning" genital warts: there is now a better treatment for genital warts that doesn't involve surgery or pain. It works like an alarm that prompts your immune system to get the warts. See
Aldara.