Yes, you can change it. You just need to make sure you are running the same radio frequency in the new one as you are now. I'm assuming you're on a 27 mhz AM system. Now there are multiple channels on that system so you need to make sure you have the proper crystal in your new pistol style transmitter. I think there are like 6 choices that start at 26.995, 27.005 etc. Something like that.
Yea, as mentioned, you can change to a Pistol grip transmitter, but ya have to get one that uses the same freq. as the reciever (rx) in your vehicle. (Probably an AM 27 or 75 MHz) Or you can intall the rx that comes with the new transmitter (tx)..) If your buying a new one, just make sure you get one that has enough channels.. Alot of rc cars use 2 channels, so anything from 2 on up is ok, but if you have a model that needs 3 channels, you'll need to get a 3 channel, or higher, tx/rx.. Confused now? LOL.. Welcome to the hobby!!
Note: Also know that there's now 2.4GHz transmitter/recievers available.. There usually a little more $$ than the AM or FM tx/rx systems, but you dont have to worry with crystals and stuff, and the antenna is a stubby.. (You can tell an older AM or FM transmitter by the telescopic antenna..)
From the same website you posted: http://www.modelsport.co.uk/?CallFunction=ShowSpecification&ItemID=28015 Looks like a pretty good 2.4GHZ transmitter with reciever and 2 servos.. Looks like a good deal for a 2.4 system. But if your tight for cash you can get a basic AM system even cheaper..