If the shiny is randomized for each individual player like regular field research, then you will only have increased chance of it being shiny if you claim the reward during the window. It will drop to the regular shiny rate if it is claimed after.
If the shiny is fixed per pokestop guaranteed for all players that spin that pokestop like Squirtle CD research, then the shiny is only guaranteed if you claim the reward during the window. Again, it will become a regular random shiny chance after.