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I have been watching a couple of Steven Raichlen's episodes of "project smoke".
In a couple of them he uses a brine of cure #1, salt etc and boils this mixture to make it easier to dissolve.

I have always been scared to do it that way.
I may boil to dissolve salt and sugar but I only add the cure when the mixture is cooled down.

What I would like to know:
Can you safely do it his way, or is it better to dissolve the cure in a cold/cool brine?

Dissolve in cold water. It's possible for sodium nitrite to degrade to NO gas and be lost in hot water especially if the water is slightly acidic. Your way is correct.

Thanks,
It's nice to know I am right every now and again

Hint to save time cooling:
Bring to a boil your ingredients other than cure in a small amount of water, just enough to allow them to go to solution, then mix that hot mixture into a larger batch of cold water, do the same with your cure, mix in a small amount of cold water, we like to do that as we can visually see that the cure has dissolved. Pop that into the large batch and top off with cold water to the exact batch amount. Saves a lot of cooling time that way, just make sure you use enough water so that the ingredients can go into solution.