Is there a relatively inexpensive form of double sided tape that would be safe to use (i.e., low static) for mounting a sensor?
You will need to use ESD Kapton Polyamide tape single sided tape.


Seal all exposed surfaces and conductor joints
Use for adhesive to material


http://www.tapemarket.com/esd_tape.htm

Warning : it is not really cheap but that is what is used in PCB industry. Banggood has it.

If you really want double sided tape. So be it but then you risk non conductive high e-field damage.