These are great questions. On average, there is probably less than a 1 in 1,000 chance you would transmit your oral hsv1 infection to your partners genitals during any given episode of oral sex assuming you avoid oral sex when you have an active cold sore or feel one coming on. Now, this is "on average" and you may not be average. Your 1-2 outbreaks per year is probably higher than normal. So, it is very possible that you asymptotically shed the virus more than average. How much more is difficult to know, but most transmissions are due to asymptomatic shedding of the virus.
The best course of action is to communicate your concerns with your partner and let him decide after he's fully informed. Statistically, at least 50 percent of your partners are going to already be infected with hsv1. Thus, they are immune or at least very highly resistant to another infection elsewhere on their body. Is your partner already infected? Most people hsv1 infected people do not know they are infected and are quite surprised when they test positive on a antibody blood test. The reason is because most hsv1 infected have been infected since early childhood and never get outbreaks or very rarely get outbreaks, like every 7-10 years.
As I understand, antivirals are not as effective on hsv1 as they are on hsv2, but they still reduce viral shedding. Your partner may want to get a blood test done with the caveat that the IgG test does misses somewhere between 10-30% of infections. If he tests positive on it, he is infected and just didn't know it, and you will be able to lay your concerns to rest. To get the most accurate results, you'll need to get the Western Blot test performed.
Most people that get infected with genital hsv1 experience very few outbreaks and a good percentage never experience another outbreak after the initial outbreak.
You are to be commended for being this responsible and thoughtful about your partner's well-being.