If you successfully evade a monster can you then chose to fight it (combat check) without having to take a horror check? I am interpreting this from the last sentence on page 14 of the rule book "If the investigator successfully evades the monster in the first place, he never needs to make a Horror check at all." Tactically therefore this would seem to be a good option if the investigator has a high Sneak value (better chance to hopefully evade the monster) and a high Fight value (to hopefully kill the monster).

If you Evade, you don't Fight because you chickened out from that combat. So, nope, you can't