Hi Raaz,
I wouldn't assume to speak for Harvey, but in that he stays quite busy, it may be a little while before he sees your post and is able to respond to your question. I have sat with him at his home through several days of grafting multiple cultivars, and can give you what he taught me about relieving the sap flow.
If fluids have begun to push through your host plant, Harvey makes several superficial cuts, just below the grafting site, through the outer bark, and just into the cambium layer. These cuts are not quite around the entire circumference of the trunk or branch being grafted onto... but rather they encompass about 3/4 to 7/8 of the circumference. The several slices are just 3/8 to 1/2" below one another, and the non-incised portion are offset from one-another. (The uncut portion of each slice is not immediately above or below the next uncut portion. If you are familiar with automobile engines, you could substitute the piston rings for the slices. The opening of each piston ring is set 1/3 offset from the next ring on the piston)
The plant is not kept from its watering regime. (Don't stop the appropriate watering of the plant, but remember that the foliage is no longer present on the plant, so water requirements are drastically reduced as evapotranspiration has all but stopped.)