We have storage type vessels containing powder only, such as catalyst, but under pressure from the inlet, and it fit to the limit of Div 1, so we stamp it. I do not think content is a factor to exempt from stamping.
However, it seems your cylinder is only a mechanical part to take the occasional pressing load as pointed out by other people, not really a pressure containing equipment, then you don't need to stamp it. If you have doubt, you can talk to qualified U stamp vessel shop.
Just curious what kind of shop will fabricate the cylinder, will they provide code calculation? what NDE will be done? any certified ASME material and test report ? any third party authorized inspector(AI) involved ? You all need these to get a stamp if you want.
When you stamp a vessel, and later on you want to modify the pressure part, you will need proper code calculation and details for AI to review to get a R stamp, very tedious.
There are many pressure containing cylinder without stamping, which you will see around the street on a truck bed, such as propane, oxigen cylinder, etc that people use for welding and many other purpose.