Could this be as simple as copying and pasting "show run?"
In general, yes. You will probably need to edit the interfaces because the stackable switches will be something like
GigabiteEthernet1/0/1 (Switch/Slot/Interface), but older switches may be something like
FastEthernet0/1 (Slot/Interface). You can verify the interface name differences ahead of time.
There may also be a few minor things, e.g. trunk encapsulation support (some older switches need to set the trunk encapsulation, but most later switches only support 802.1Q, so the command will error), but they normally do not cause any real problems (assuming you are not using ISL, which newer access switches do not support).
Your best bet is to copy the configuration from an older switch into a text editor, then fix the interface names and try to paste a chunk of lines at a time into an off-line, newer switch. You will see where you get errors, and you can fix those in your text files.