You can do 1/4" BB, but there are caveats.
Glued butt joints adhere to the upper-most layer of veneer on the plywood.
1/4" is mighty thin, and there ain't a whole lot of meat here.
A concussive impact can shear the top veneer layer right off.
Consider using cleats on the butt joints.
I use 3/8" BB routinely, and that size still requires a lot of careful attention to detail.
1/4" panels are going to buzz without sufficient bracing.
I suggest no more than 3~4" of span between braces.
X-Y-Z bracing is a huge help.
Opposing panels connected to each other with a cross-brace will cancel each other's vibration.
As noted above, 1/2" BB (0.447") offers a lot more meat in the panels and joints.
You can safely span 6" between braces without fear of buzzing.
When I die, I hope my wife does not sell all my toys for what I said I paid for them...