Brandsurge and weapon switching questions

Okay...so the way I understand it, there's a delay between casting Brandsurge from Witchhunter's Judgement and actual explosion, based on targeted brand remaining duration. So you could switch weapons during that time.
What happens then? Will the Brandsurge use my other weapon's stats for explosion, will it "snapshot" the conditions when casting Brandsurge, or will it somehow fizzle as Witchhunter's Judgement is no longer equipped?
And will Brandsurge cooldown recover while I'm using the other weapon?

Edit: oh, and related, what tags does Brandsurge have? Does it count as brand skill?