Then I would merely add Bennies to the game, no need for characters to spend precious edges for Bennies..
Just house rule up some bennies:
everyone gets x MORE bennies
a pool of bennies for everyone to use
having more bennies will give characters the confidence to do more exciting things.
you could also create new bennies.
like a benny that lets you re-roll damage.
or a benny that, when spent, counts as an auto ace on the skill die for that roll, and the roll you make starts out at the second tier. (if a skill is at a d10, the player spends the benny, and starts rolling as if they already rolled an ace, so the minimum result would be an 11 in this example).
I guess I what I am trying to say is that there are ways to adjust the game without a lot of extra edges to remember. Although, new benny types are new and have to be remembered..
Just some thoughts, that's all..