Confusion about reduction of $L=\{w_i | M_i\text{ halts on }w_i\}$ to Halting Problem or Diagonalization language?
I want to reduce $L$ (stated above) to the Halting Problem in order to say that L is recursively enumerable


So far, so good.


  but not recursive just like the Halting Problem


Here we have a problem. Reducing $L \leq_m HALT$ does not prove that $L$ is not recursive. Actually, all recursive languages reduce to $HALT$!


  but is it enough to say that if I can solve the Halting Problem then I can solve $L$


No, this is not a may-one reduction argument. Indeed, if you can solve $HALT$, then you can also solve its complement. This however, does not imply that the complement is r.e., otherwise we would get that $HALT$ is recursive.

You need to define a (total recursive) reduction function from $L$ to $HALT$.

Then you need to prove that $L$ is not recursive. For that, you could prove the opposite direction $HALT \leq_m L$, constructing a reduction function from $HALT$ to $L$.