You'd better not use the organic electrolyte in environmental atmosphere. The organic solvents are easy to adsorb water, which would affect the charge-discharge results. For example, the CV curves may show additional peaks of water decomposition at the voltage above 1.2 V.
Yes, it is possible to (test, and maybe to) operate, after a long time drying in an oven, the Lithium perchlorate (in ACN or PC) under, at least, the 2 basic constraints, below; so, you can exercise:
1) in a well sealed cell, with your super-Capacitor electrodes, and restrict the Potential test range of your cell, only[1],
2) within a low (and safe) nominal Potential range, up to Vmax ~ 1.2Volt[2,3] versus SHE (Standard hydrogen electrode).
1. For your supercapacitor electrodes this constraint (Vmax) might be (much) less than (Vmax- (-Vmax)=2*Vmax), since the ref. value of Vmax is versus SHE ref. electrode, e.g. not your CE electrode (CE, for a 2-electrode cell).
2. The constraint (Vmax) might be splendidly operate even in the extreme V-window of the: 2*Vmax = Vmax- (-Vmax), as the activity in the elegant example of the Lead acid battery[3] (single) cell (max. operation, safe-window, Voltage ~ 2.2V ~ 2*Vmax).