It seems like you should be fine, one inch is not particularly deep and 4 months is not very long. I would just rinse it and add it to the top of your new sand bed (assuming the new tank will have more sand than the old).
If the sand were older/deeper, I would just abandon it completely and get new sand. If the old tank has a significant amount of live rock that is also being moved to the new tank, the live rock itself likely has enough bacteria to avoid a cycle. I moved a 90 to a 180 and left the sand behind, only moving the rock and livestock to the new tank and did not have an observable/measurable cycle. Nothing lost other than corals which were accidentally broken in the process.
Matt