cut through the pith (center), if it is a branch then the pith is probably slightly off-center, this is more obvious with large branches. If you include the pith or wood near the pith in the blank it is a lot more likely to crack. I would cut into 4 pieces. Remove the bark, paint the ends and weigh each blank with a kitchen scale. A week probably isn't enough time to air dry, which would result in the least cracking. I personally would put them in a food dehydrator and hope for the best. 24 hours is probably enough, but weighing every 6-12 hours or so will tell you if the weight is still dropping. If you use a food dehydrator or toaster oven, you will want to let the blanks sit for a couple of days indoors to get back to equilibrium moisture as they will probably over-dry. Elm is notorious for cracking, branches tend to be worse.
Edit: other drying options -- hot car window, HVAC return, warm window. Basically heat and air flow are what drives the drying. Another option is to boil the wood in water, this relieves stresses and reduces cracking when force drying in an oven. Lastly, you can soak smaller pieces of wood in denatured alcohol or other solvent and then dry - this basically leeches out the water (fire hazard, so use caution).
