There are I’d say three common options for brazing steel
Manganese bronze, a general purpose rod that needs about 900 degrees, good filling capability
Nickel bronze, a high strength and wear brazing material, needs more heat, great for teeth on gears or bushings.
45% Silver, good strength, needs about 650 degrees, requires close fitting components and cleanliness. Rods are more expensive
For your job I’d either pick manganese bronze or 45% silver. Manganese Bronze needs more heat and you’ll struggle with heat but 45% silver does need good surfaces that are close fitting. If you’re prepared to do the work to get a good close fit and clean up thoroughly I’d go with the silver.
The brazing fluxes are usually high or low heat or paste vs powder choices. Basically borax to prevent oxidation and aid flow.
If you go with the 45% silver a standard paste flux will work. If you are using the manganese bronze a “Tenacity” flux for higher temperatures will be needed. For pipe-style work I’d use paste flux.
With this job if you’re using an internal sleeve I’d probably trim the handle so that there is a slight gap where the sleeve fits. This way you can get the filler in both sides and once filler rod has wicked up well then fill the gap with more braze. After it’s cooled you can grind the filler back to get a smooth surface before etch priming and painting. Clean off all the flux and muck before paint or it’ll just blister and peel.