First, drop yeast/hop sediment from the cone, as much as possible. Then add your priming sugar solution. Then attach a CO2 line to the cone valve, turn on the CO2 to about 5 psi, open the top for venting and bubble CO2 through the beer for about 5 seconds. This should mix the priming solution pretty well. If you include fresh yeast in your priming solution then O2 damage will be minimal to none. If it's a hoppy beer, you may lose some aromatics doing this, but it's a good way to mix stuff into finished beer (sugar, finings, etc.).