You can publish your map and have the friend play it in Arcade or even download it and play it in the Editor.
Then, in the Arcade, you can select your map and the last option should be Request Deletion (or something like that). However, keep in mind that the deletion is not automated and someone from Ubisoft would have to manually delete it, so who know if and when will that happen.

If your friend is geographically close, you could also save your map on a USB stick and give it to him, but, because maps are tied to the PSN account, he would have to log in with your account on his console in order to load the map.