Solder will flow towards the hottest part of the job and potentially solidify on to any part in the heating zone that has flux on it.

In jewellery fabrication, it’s particularly important to control solder flow. This is done in three ways: the judicious and sparing application of flux, using pallions of solder or balled-up solder placed on the work before the job is up to flow temperature, and the painting on of solder flow inhibitors such as liquid paper.

I’m unclear how big the job is so can’t really advise on the size of torch/burner you’d need.

Place the wheel flat on a piece of vermiculite board. Place barrel in place and apply minimal amounts of solder wire pieces on the inside up against the joint. When heated the solder will wick into the joint by capillary action but not go outside the joint as there is no driving force for it to do so, unless you have put silly amounts on to provide a pressure head. Any mess will be on the inside out of sight.
You could also use a flat piece of steel to put it on and heat from underneath but it is harder to get the tube as hot as the wheel at the same time.
If the inside is to be visible because it is crossed out the solder can be prevented from flowing along the arms using a barrier paint (tippex) but test first that it holds up under heat.

Modern Tippex not so good.

Before there was Tippex, ancient fossils used Milk of Magnesia to mask soldering jobs. No idea if that is still available? Probably rebranded as some expensive acid reflux cure.