You can buy smoker fuel, or like me use pine needles and sticks.... cardboard would be ok I guess, but remember, glue might be used in them and might not be safe. Egg cartons? Are they cardboard? Wood shavings would be best.... corn cobs- I guess... never tried that.
I don't get in my hives alot. The more you are in them the more bees you will lose and the more you will weaken the hives. I have many hives I never wear anything with and never have to smoke. However, I have a few that if I just go in without smoke... look out! I do just as you do... smoke the front and top and then I wait only for a couple second and then open and go in.
Yes I go in... we sit and have tea w/ honey and the queen and I chat and have a good laugh. We make fun of the drones....:lpf: