Welcome to PA. First thing is there are no stupid questions here. Only unasked questions are stupid.
When I build a bow I make it symmetrical, equal length from the center of the handle to each limb tip. I make my handles 4" long with 2" each side of the center. For the arrow pass I put my middle finger on the center of the handle and grip it. The arrow pass is at the top of my hand. Brain tanned leather makes a very comfortable handle. You can do as you said with a 1" wide and wrap it around the handle area tucking each end under the wrap. If you wrap it tight enough you may not need to glue it but you can use contact cement on the handle area and on the back side of the 1" strip but be careful when you wrap it because when the 2 glue surfaces touch they will be stuck. Also remember to wrap the handle the direction your fingers point or the wrap can be loosened just by gripping it.
I like to use a Floppy rest(the idea of Mickey Lotz) at my arrows pass to protect my hand and to quiet the arrow. Below is how I make a Floppy rest...
