If memory serves, you only really get the slight bubbling and sizzling with a more recent leak. I think the longer it's been spilt then the weaker the reaction. This makes sense as the alkaline substance gets weaker as it dissolves whatever it can, and the air will carry some of it away too (and spread it in the vacinity unfortunately). If you wash the board without first neutralising it then you risk spreading the leakage onto other areas of the board (rinsing for example).
So, it would be your second option, but I suppose if there's no sizzle then the alkaline leakage isn't so strong and you could wash it away thoroughly with a clear conscience. I like to use a toothbrush and plenty of running water. I live in a hard water area though... you can't win 'em all I suppose! IPA to then clean the area again and also remove the sulphites from the water. Then I'd probably rinse it again with my hard water even though I shouldn't. I don't take it too seriously to be honest, as long as I know it's clean and I have washed away the leakage and the board is clean then I'd be happy.
Plenty of dry time too before power on due to moisture under IC's etc. We just have to be sensible and I don't think you can go too far wrong. Don't use a hair dryer or similar because that would induce static. Just be sensible about things and it'll be fine.