Do bother with caps.
Sorta.
If you tried hooking that up to a transformer, say to put 1.00A into it so you can measure the winding's miliohm range resistance, you'll end up with an AM transmitter rather than a CCS.
I would recommend bypassing the input to ground, and putting an R+C across the device, maybe 100 ohms + 0.01uF. That won't wreck the CCS-ness too much (at AC) while keeping it more stable into questionable loads like that.
Best values are hard to guess at, and depend on the particular load. Just checking that it isn't oscillating is probably fine. To really evaluate it, you'd need to pulse it somehow and watch the ringing with a scope, which probably isn't worth the trouble.
Tim