Brown black red instantly points to a 1k resistor, but I wouldnt expect them to be that large a power rating (going by their physical size) in that application, as you'd need more than a few volts to run them at their max rating.
My color recognition isnt very good, they look a bit like brown black brown to me which would be 100 ohm, and more inkeeping with the physical size for something running off batteries, or they could be 100uH inductors (or 1000uh/1mh), if this thing is a shock collar then its quite possible they are supply decouplers or the high tension generators (there looks to be a transformer on the left so supply isolators is more likely).
Go ahead and solder them back on, it shouldnt be a hard job at all really, just be carefull not to make any solder bridges.
If the part is dead and you cannot scarf the insulation back to get a solder joint, to find out for sure whether its a inductor or resistor, remove the device and scrape away at the paint and keep going till your nearly half way through, if you come accross very fine winding wire its a inductor, if its just white or dark coloured hard stuff its a resistor.