I guess you need to use the sonicator to release your intact protease from the cells unless the proteases are extracellular enzymes. Are you going to purify  proteases prior to perform activity assay? or Are you going to detect protease activity using tissue homogenate/cell lysate? If you are using tissue homogenate/cell lysate for protease activity assay, it may not necessary to add protease inhibitors to the lysis buffer.

If you add protease inhibitors to your tissue homogenate, you may inhibit the very protease(s) you are trying to detect. Don't use protease inhibitors unless you are sure that your particular protease is not affected by them.