Staking also isn't some revolutionary great plan either. It is widely believed/known that runescape can track all of your trades and stakes. So, basically this means staking and just trading straight up are the same thing. Regardless of you killing a mule or just trading to a mule, RS is going to see that it's all coming from X account to another X account. Like many have said though, I don't think you are going to get flagged for RWT unless you are moving 50m+ daily across accounts.
From what I've read in the past from mods, the only thing that they do not track is dropping items/cash. This means that drop trading is likely the only method that can keep you completely safe from a RWT ban.
In conclusion, do not worry about it. I've been moving money across accounts since I started playing RS in 2005 and I've only received ONE RWT ban over that 10 year span (The RWT ban came on an account that was previously permed for a year for botting as well).