You can whisk the coffee manually if you do not have a stick or hand blender. This would require more effort and time.
If you don't like it ice-cold, skip the ice cubes and add warm milk into the glass.
Whipping coffee just before you want to drink it is the best option but if you want to make it once and store, it stays in an airtight container for a week. The texture won't be as good as the fresh version.