I think it's been different depending on the following:
Exposure time - how long was he exposed to the Kryptonite?
What type of exposure - how close was it? Physically touching him or grazing him or a few feet away.
Each exposure in the show was different. At first in GGOH it lasted a few days and the adrenaline of being in danger helped speed up his recovery. Then there was the exposure in the Kryptonite cage where we're assuming he was powerless and yet still attempting to fly to save the man that nearly killed him. Off-screen recovery there but we have to assume that was at least a day he was in the cage so let's assume the recovery time was much longer than GGOH. Then there were incidents of Kryptonite exposure where he was exposed at a distance and was fine the next day like in Metallo. The recovery time was near real-time with lingering soreness.
How he heals may be going into further detail than necessary but a few things to consider as you develop the scenario for the scene. Exposure time and proximity are important factors that impact how he would recover. In cannon and in other comic-based movies and shows the healing is showing the physical injuries recovering. My personal opinion is that these would happen at the same time however it's open to interpretation. Remember he's alien not human. So the way the human body would recover would be different, however, the absorption of the yellow sun speeding up his recovery would make sense based on comic cannon.
