It certainly IS possible, but it wont be the easiest project to tackle unless you have experience desoldering/soldering SMD components. The LEDs on the front panel are all surface mount LEDs. SMD components are much harder to work on then through hole components, and if you're not careful you can pull the solder pads off of the PCB.
The 'proper' way to do it is to use an SMD rework soldering station (these are very expensive), but there are "tricks" you can use to do it with a traditional soldering iron (just do some googling to find some how to articles and videos showing different methods).
As for suitable replacement LEDs; if there are markings on the existing LEDs then you could look the number up, but there probably aren't any markings on them. I suppose you could start by measuring the voltage across the LED but you will also need to find out their current draw to avoid overloading the circuit(s) that power(s) the LEDs.
You could try contacting Uniden to find out what LEDs are used. It is very unlikely that they will give you any information about internal parts (manufacturers do not want end users to modify or even open up the cases on their products), but it won't hurt to try.
Good luck
