My working population is non normally distributed and from time to time I need to take a sample of it.  Sometimes my sample exists of 100 units, at other times of 150 units. Of my sample I calculate the mean, $\mu$, and with bootstrapping I determine the SE, $\sigma_{\bar x}$. Since $\sigma_{\bar x} = \sigma /\sqrt{N}$, I calculate $\sigma$.  So far so good, by using control charts ($\mu,\sigma$) I can now see if there is anything happening to worry about.

By use of deviation calculation rules you can prove quite easily that the formula  $\sigma_{\bar x} = \sigma /\sqrt{N}$ also can be used for non normal distributions.  

I play with the idea to make control charts using the trimmed mean and the 70%-value.  Now I am not so sure anymore. (Frankly, I have my doubts whether you can do this for normal distributions as well.) Can I use the same simple trick to remove the $n$ from my equation?  

Let me put it like this:  Is what I am writing valid? 
$$\sigma_{70\%} = cte * \sigma / \sqrt{N}$$ with a $cte$ independent of the value of N?
$$\sigma_{\bar x_{70\%}} = cte * \sigma /\sqrt{N}$$ 
with a $cte$ independent of the value of $N$?

To use my control charts I don’t need to know the value of my $cte$.  For my s-chart I can just plot out $cte* \sigma$ in function of my sample number.  But I really need to get rid of the $N$!

I hope you understand what I am getting at.  I would already be happy with a yes or a no, you can not do that anymore.  If you can direct me to a place where I can find more information about this problem I would be even more grateful.