I am not sure you CAN get a single screenshot showing the map AND events, without all the gridlines.
One way is to take several screenshots in the editor, crop away the gridlines from one of them and overlay it on top of the other (so you get the map without the lines), but the events will still look like boxes.
The other way is to do it as you're playing the game, but that will require lots of screenshots, and putting them all together in another program, removing the PC from each screenshot as you go.
Both methods are messy, but as RM2K/2K3 does not have any scripting functionality, you're limited to what the engine offers you, which is nothing.