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Past work on this topic & References
There are remarkably few papers on this topic [conductivity used to monitor enzyme catalysis] in the literature (at least that I have been able to find that are relevant to the present work). However it is hardly a recent topic, since Henri used the method to measure gelatin hydrolysis by trypsin in 1903! Conductimetry has been widely applied in micro-biosensors, but I have excluded these (with an exception at the end) as they are 'High-Tech' & do not involve measurement of enzymes by conductivity change. A recent check shows no papers added since 2015.
For an excellent general text on enzyme assays I would like to refer you to the book of this title edited by Robert Eisenthal & Mike Danson
(see Google for online version)
This book contains a chapter written by my PhD supervisor Keith Brocklehurst
I also authored a book 'Molecular Enzymology' with Robert who was a very clever & original guy who devised, by lateral thinking, the Direct Linear Plot for kinetic analysis
Enzyme catalysed reactions measured by conductivity changes
Urease: (this paper is in French)
Hanss, M. & Rey, A. (1971) Biochem et Biophysics Acta, 227, 630-638
Cholinesterase: (this paper is in French)
Hanss, M. & Rey, A. (1971) Biochem et Biophysics Acta, 227, 618-629
A wide range of enzymes: This very useful paper is available online see link below
Lawrence, A.J. & Moores, G.R. (1972) Eur. J. Biochem. 24, 538-546
conductimetry in enzyme studies
Hill, G.R. & Tomalin, G. (1982) Anal. Biochem. 120, 165-172
Microchip assay for alkaline phosphatase:
Faure, M., Sotta, B. & Gamby, J (2014) Biosensors & Bioelectronics, 58, 61-67
Kechadi,M., Sotta, B. & Gamby, J. (2015) Talanta 132, 785-789
These last two references demonstrate the 21st century micro-technology approach to the topic, where reaction volumes are in the low nanolitres and there is no direct electrical contact with the reagents. Fancy kit is needed to fabricate the chips but it could be done on a large scale to give an inexpensive device such as the modern glucose analyser