So many ways to skin a cat! If you really want to soft solder it, you will as previously stated have to thouroughly clean off any traces of zinc, use of a grinder is beneficial. When this is done, I would be inclined NOT to use wet N dry paper to clean the surface, the paper appears to ingrain the steel with small particles which repel solder, with the grinder the freshly ground steel surface is more pure . I would also use a good acid flux such as that obtained from a plumbers merchant.
The next most important aspect of this job is temperture control, I suspect you will use a blowtorch and this is something you should be very careful with because if you raise the temerature of the steel excessively it will begin to 'blue', form a scale and no soft solder flux in the world will break it down. With careful control of the heat you will be able to solder it but it is tricky and experience here counts for everything.
Give it a whirl, if it fails you will at least have tried and will learn something from the experience, in anycase, you can re-grind it and have several go's at it until you succeed.
Personally I would reach for the brazing equipment every time but this or other options may not be available to you .
It can be done so stick with it (no pun) and good luck.
