I'm guessing that you have some VBScript / JScript customization skills with ArcPad, if not, it'll be harder to guide you. The rough code outline is:
1. Create a Point object in the current map projection using CreateAppObject
2. Initialize it to your X, Y coordinates
3. Create a Coordinate System object
4. Initialize it to a Geographic Coordinate system (e.g. set it to the WKT string of WGS 1984)
5. Use the Coordinate System's Project method to reproject your coordinates to Geographic coordinates
6. Update the script to use Geographic X, Y for Longitude, Latitude respectively