That's up to how secure you want to be in the knowledge of not having anything to pass on.
Chlamydia and gonnorhea are much more likely possibilities although extremely small chances.
HSV2 is practically a zero chance here.
If you want to make absolutely sure, then you need to test observing the appropriate window periods.
therefore I can confidently have sex with my wife?
If there is no virus present on the skin then no it cannot infect another. It is not always possible to know when the virus is present. As mentioned HSV2 is only a theoretical risk in this circumstance.
you mean no transmission can occur when the virus is dormant?
Practically zero.
HSV2 infections are rare, although we are clearly talking about someone who has a higher than average chance of an oral infection.
Even with one, the virus sheds maybe 3 days a year and it is questionable whether there is sufficient viral load to cause infection on all 3 of those!