Just knock it out into the bedding and proceed. Believe me, it will not go to waste...they will scratch for it and glean it out of the bedding. If you'd like to make it easier for them,place a flat board or something similar nearby on which to knock out the old feed. Nothing goes to waste with meaty birds.
Have you elevated your feeder and placed wire over it so they cannot walk into it? This will help tremendously and you can even do some training while you are there and they are eating by knocking the ones trying to get into the feeder off of it...I've done it and while you are standing there they will pretty much stop that behavior if you are consistent.
Other than that, the shavings won't hurt the feed or them, so you could just leave them be and feed on top of them.
You could maybe tack or tape a trash bag at the base of the cone on three sides to form a funnel down into your trash can...it can contain most of the blood. I don't try to collect the blood because the rest of the chickens are all waiting at the base of the tree to drink it and so it gets used in that way.
I place my cone level with my chest so I don't have to lift heavy birds very high and the neck is at my waist level where my hands naturally hang so there won't be undue strain over a full day of processing...that lifting heavy birds over and over and hand work can get tedious after doing many in a row. Ergonomics are my thing~I've always loved a smooth flowing work place designed for less waste of motion.
You might want to rethink that....the first time a chicken flings blood into your eyes and hair and you can't step back because you are seated, you may decide that sitting in front of a twitching, flailing, bleeding stump is probably not the way to go.