To go a little further in repsonding. Yes you can directly swap the CPU module. It is not necessary to make any changes to the chassis.
The only thing you might be a little careful of, is that the 5/03 probably draws a little more current than the 5/02. If your power supply was already maxed out, the extra current draw may put you over the max current available.
If you have RSLogix 500 available, open your project file and then open the I/O Configuration. There is a little button there that I think is labelled "Power Supply". This is a little estimating tool that shows the total current draw for the modules in your system and then you can select a power supply and it will tell you if it is overloaded or within margin.
OG