I do not know which kind of experiment you have planned. Anyway, It will depend on which kind of purification will carry out later. If you are worried about the sonication you can try with Lysozyme, but you must take into account the increase of protein for specific activity. If you are going to compare expression of recombinant protease may be you add some chaotropic agents or simillar if you compare with not recombinant cells, activity will decrease with this kind of agents. Another method will be physical breaking with glass microballs, if you don't have a Braun homogenizer system you can perform with vortex, but try to keep as cool as possible. Of course you must not use DTT, PMSF or EDTA, but it will depend of which protease are you interested as they are cystein, serin and metalo-protease inhibitors .
If you have bacteria, you can use cell lytic or some othe lysis solution, and sonication. This is super cheap and works to fragment the DNA into smaller pieces for easy purification. Since you have a cysteine proteinase, definitely have DTT or the equivalent in the buffer but no higher than 5 mM if you are to do NINTA purification. The buffer to lyse with, should be based on other cysteine proteinases that were purified in the past. And in the buffer have a proteinase inhibitor cocktail, but leave out the E-64 and other cysteine proteinase inhibitors. I would use AEBSF instead of PMSF. It is water soluble, and use EDTA, and pepstatin, and any cheap ones you can find, like trypsin inhibitors, etc. if you do Ni NTA, remove the EDTA.
To follow the proteinase activity, I would use a peptide substrate assay in combination with a known inhibitor of either your protein or cysteine proteinases. If you have a HPLC and know the cleavage site, then a DNP labelled substrate can be used to determine if the correct product is being produced. You can use a standard peptide that is the cleaved piece to run as a control. This is cumbersome, but will allow to to follow the right specific activity. And always do the reactions with the proteinase inhibitor cocktail, minus and plus your specific cysteine proteinase inhibitor or something like E-64.
You can use a FRET based peptide substrate as well, but this doesn't tell you where the peptide is being cleaved. But do minus and plus inhibitor. Otherwise, you may not purify the right protein.