When I got my bare-root grafted adeniums last year I asked and was advised against cutting the stems. Except for one plant that produced a branch below the grower's cut, as well as one close to the cut, the stems of the others produced only one branch each and some of those grew over and on top of the stems. I had wanted more branching...but sometimes the genetics of the plant and other factors will not allow this.
If you do decide to cut, I would wipe up the sap then apply Elmer's outdoor waterproof glue to minimize scarring and to protect against rot. A lady at the flea market told me she uses clear nail polish...haven't tried this one yet. I don't think cutting will compromise the graft.
It is not unusual for the caudex to produce new growth buds...simply cut it off with a clean, sharp knife, and let the caudex callous on its own...don't let it get wet. Some may recommend dusting with cinnamon or sulphur as an anti-fungicide. Adenium growers don't do this, but I tried it once and the caudex scars turned dark so I had to re-cut to remove the dark scars.
Hope this helps.
