http://www.remington-products.com/manuals/ib_mftitaniumu.pdf
In the PDF instructions it describes how to remove the batteries. The instructions fail to mention that there is a spit of yellow glue that is holding one of the batteries to the curcuit board with a death grip. Undoubtedly, you will have to use a knife, not in the glue, but on the skin of the battery. Pull on the teather wire, and slice the battery skin around the glue.
If after removing the batteries, and you are not thouroughly discusted with the manufacturer, then purchase a couple of AA Ni-cad batteries solder the positive of one battery to the negative of the other. then solder the free positive end to the red wire, and then the blue wire to the free negative end. Then try to remember how to reverse the process and put it back together, without leaving any parts out. ;-)
There is a risk of injury by overheating the battery when soldering. That should be avoidable if you remember how to drop solder. Just like its name, it involves having the wire securely held in place. Then hold solder iron over the wire/battery end. Then take some rosin-core solder and apply the solder to the hot tip. Then make sure the newly melted solder lands on the contact. Keep in place until it cools and holds the wire to the battery.
If you think this is better than writing to Remington complaining that they did not make it easier and use contacts, instead of solder, so we can simply pop in a new set of batteries. Or maybe look at other manufacturers, and see if they are any better.