You don't have to use a sandwich maker to produce a toasted sandwich. A ridged grill pan will do.
I think packet white bread is good in this context. The sandwich above consists simply of buttered bread with slices of cheese in the middle. I buttered the bread on the inside; but I might also try buttering it on the outside, as I have to do when I use the sandwich maker. I set the flame under the pan to low/medium.