Let me answer the question that I believe you are trying to ask. Namely, if we can make a regular cardinal $\kappa$ into a singular cardinal $\kappa$ by forcing of size at most $\kappa^+$, without collapsing any cardinals, must $\kappa$ be measurable? 

The answer is no. 

The reason is that it is consistent (relative to the existence of a measurable cardinal) with ZFC tat there is a non-measurable cardinal $\kappa$ that becomes measurable in a forcing extension, by forcing to add a Cohen subset to $\kappa$. This is explained in my answer to the question [Can measures be added by forcing?](http://mathoverflow.net/questions/110871/can-measures-be-added-by-forcing) Furthermore, one can arrange in that argument that th GCH holds, and that there are no other measurable cardinals.

So suppose that $V$ satisfies ZFC+GCH and there are no measurable cardinals in $V$, but $\kappa$  becomes measurable in $V[g]$, where $g$ was $V$-generic for the forcing to add a Cohen set $g\subset\kappa$. This does not collapse cardinals. Since $\kappa$ is measurable in $V[g]$, we may now perform Prikry forcing over $V[g]$ to add a Prikry sequence $s$, which changes the cofinality of $\kappa$ to $\omega$, but does not collapse cardinals.  

So in $V$, there were no measurable cardinals and $\kappa$ was regular, but the combined forcing $g\ast s$ made $\kappa$ into a singular cardinal without collapsing any cardinals. This combined forcing has size $\kappa^+$ under the GCH.