Can you give yourself genital herpes by touching your cold sore than your genitals? or is it rare since you already have the virus/antibodies already?

Not so rare: If you have active lesions you can cross transmit the vires from one location to another.

You can't: They are in the same family but inhabit different parts of the body. Thus you would not be transmitting HVI from the lip to the genital or vice versa.

Yes: You can if you touch the liquid of blister and touch the skin of your genitals.Though the herpes type 1 usually causes cold sores it could cause genital herpes as described