Advice for getting a loose neck to fit better

I recently received a kouki shamisen, but I haven’t played it yet because the skin is ruptured. However the neck is very loose in the dou. It has a slight movement which probably will mess with tuning and just be unpleasant. I am wondering if anyone has an ideas to fix this on the cheap? I was thinking of cardboard, but I&m not sure if that would have any adverse effects.

Any experience/advice appreciated!

I would suggest to wait for the skin, so you can check the string to skin and sao distance before you do any shimming as it might affect it in wrong direction. Also, then you say it is loose do you mean the sao can be moved relatively to the dou when inserted all the way or just easy going in?

It can be moved even when its all the way in (rotate a few mm). There is literally zero friction when inserting the neck.

I see. Looks like the square hole in the dou is a bit big. It is possible what the sao originally from another instrument. Personally I would try to shim the square hole with 0.5mm thick or less veneer pieces on all 4 sides, so the center of the hole stays the same

Or at least 2 opposite sides

I would suggest: try some seconds glue/ super glue, preferably the gel variant.

Agree with gluing some veneer to shim it up. Maybe all around or on the top/bottom or sides if it is moving only in that direction. if you glue it well and clamp it you could go a touch more than needed and then sand/file it down to fit. Or maybe it will fit first try!
If in a pinch and no veneer around you could even layer and glue paper.