Here is the standard argument: you can decide whether it is prettier than the one you had in mind.
Let $V_{\ell}(E)$ be ${\mathbb Q}\_{\ell}\otimes\_{{\mathbb Z}\_{\ell}}T\_{\ell}(E)$; it is a two-dimensional ${\mathbb Q}\_{\ell}$ vector space. When $E$ has CM by a quad. imag. field $F$, it is free of rank one over $F\otimes\_{\mathbb Q}{\mathbb Q}\_{\ell}$. Thus the image of $Gal(\bar{K}/K)$ acting on $V_{\ell}(E)$ (or equivalently, $T_{\ell}(E)$) lies in $GL_1(F\otimes_{\mathbb Q}{\mathbb Q}_{\ell})$, and so is abelian.
Note that this argument gets to the very heart of CM theory, and its relation to the class field theory (i.e. to the construction of abelian extensions): the elliptic curve $E$ (or, more precisely, its Tate modules) look 1-dim'l as modules over $F$, and so give abelian Galois reps. (Just as the $\ell$-adic Tate modules of the multiplicative group ${\mathbb G}_m$ give 1-dim'l. reps. of $Gal(\bar{\mathbb Q}/{\mathbb Q}).$)
You might also want to compare with Lubin--Tate theory, which is very similar: one uses formal groups with an action of the ring of integers ${\mathcal O}$ in an extension of ${\mathbb Q}_p$, and again they are constructed so that the $p$-adic Tate module is free of rank one over ${\mathcal O}$, and hence gives abelian Galois reps.