I would irradiate, the cKit have problems i.e. no CORIN, the Wsh are your best bet.
If you pre differentiate the mast cells before reconstitution, the mast cells do not return to all tissues. (Galli has a paper on this), but you could reconstitute with whole bone marrow.
If you look at Jax, there may be a flox cre system you cold use.
I think this will be quite difficult since mast cells are positioned in tissues... and I am anyways very skeptic about mouse models with respect to basophils or mast cells because these cells are functionally different from their human counterparts. Then the problem of functional differences of these cells between BL6 and Balb/c... (which one compares best with the human system??).
Would it be better for your purpose to block some mast cell mediator instead? Why do you want to deplete mast cells? I think there are also basophil knockout mice.
If you suspect that the mast cell molecule(s) that is relevant for your system is contained in granules, you may inhibit MC degranulation instead of depleting MC, using sodium cromoglycate (cromolyn). Have a look here
But some protocols used C48/80 as a chronic treatment before the assay for research the mast cell participation on process. The intention is finish with the mast cell content.