I've been investigating the possibility of running the H9 pedal off of a portable battery. I have close to zero clues about voltage concerns, and really don't want to damage my pedal. Obviously. So I thought I'd reach and see if anyone has some insight here.

H9 requires 9-12V DC and 400 mA. I think this might be something you want:

It seems that it can meet your need. I've never used it though. Cannot guarantee how good it is.

I've used this one: https://www.amazon.com/JOYO-JMP-01-Portable-Power-Supply/dp/B00DR4FDY4

It worked but I have to say its quality is not great.