Using an electric razor alone has worked great for me. No irritation. It was the dry shave that caused it for me. Even with the shaving cream, it still was an issue to some degree, unless I used a lot of shaving cream. However, with an electric razor alone I've never had any problems. It does take longer though, unfortunately.

The thing about electric razors is that for me at least they've been no good if I ignored my shaving for a while. A more significant bit of beard or mustache (e.g more than overnight) is difficult for my electric razor to get rid of. If at any point you let it grow for a bit, use the regular razor but use LOTS of shaving cream. Without it, the irritation is inevitable, particularly with multiple shaves.