Many papers suggest just dissolving 0.1% of SDS in water.
I wonder if it is not necessary to use a buffer or if the pH of the solution should be adjusted according to the protein pH of the emulsion. (Because of the pI of the protein.)
Your point is ‘taken care of’ in the first step were the protein and oil are mixed, see for example:
Klompong, V., Benjakul, S., Kantachote, D., & Shahidi, F. (2007). Antioxidative activity and functional properties of protein hydrolysate of yellow stripe trevally (Selaroides leptolepis) as influenced by the degree of hydrolysis and enzyme type. Food chemistry, 102(4), 1317-1327. (in Google Scholar you find a free downloadable version)
The SDS step is 'just' necesarry to perform the final measurement.
It might be a good idea to read the following excellent review as well (with some critical remarks about the EAI and ESI method(s)):
Mcclements, D. J. (2007). Critical review of techniques and methodologies for characterization of emulsion stability. Critical reviews in food science and nutrition, 47(7), 611-649.