You shouldn't have any problems moving to a 7xx processor from your Celeron on that chipset.
To be sure, just make sure that 7xx procs (Pentium M) were available as an optional upgrade on your machine when you bought it. Assuming so, it is a quick upgrade if you know what you are doing, and kinda quick upgrade if you don't - but are careful. The main difference you will see (between a desktop proc and a laptop) is instead of an arm to lock the processor in place, you will have a screw that you turn 1/4 way to lock/unlock it.
If you want difinitive advice here - pass along the model number of your laptop.