So best to replace one connector (test device side) with an isolated bnc connector ?
Yes believe that should work out OK. Use the generator side common as the case ground and let the DUT side float wrt to the case and generator ground. An isolated BNC is probably the best solution for the DUT side.
Noted you have a nice Siglent DSO and AWG, you'll find some really interesting use for the Bode Function, and with the Iso Transformer this opens up all sorts of uses, see some of our posts wrt such!!
Keep us posted on your progress
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Best,