Don't think you can use those particular two with each other.. the first is a pin lock, so if there's no hole in the second adapter, you'll go insane trying to get it off.. I have that 1/2" to 1/4" hex adapter, and can't remember if there's an pin lock hole.. might be, but I can't promise.
Secondly, there will be some play in those,not a lot, but not secure and solid like the 7/16 chuck..
Your best bet would probably be to get the Milwaukee m18 1/4" right angle impact. That hole hawg may put out too much torque for a wide spade bit to withstand anyway.