I'm going to have to disagree here.
MOVIE RELATED SPOILERS AHEAD
First of all it makes Greedo a pathetic bounty hunter to have his target about a tables' length away and STILL miss. Han was preparing to shoot him to get away but he actually tries to talk his way out first. That doesn't work out and only when Greedo says he's going to kill him does Han shoot. Since he made of mention of the Stormtroppers noticing Obi-Wans' arm slicing I don't think he wanted to get more attention anyway. He knew his "cargo" was trouble, he knew Jabba was after him and wanted to slip away. Han never came across as bloodthirsty.
Leia killed the Stormtrooper at the beginning after they set their blasters to stun her. Much like Han she knew she had to fight regardless because they would try to get information from her. I remember one book I read--a Jedi series for kids no less--referring to her killing Jabba as her first cold blooded murder. It was to escape but his death took far longer because she strangled him. As far as not wanting a partner in a marriage to be set up as a killer uh, Anakin Skywalker? Yes we knew he'd become Darth Vader but tell me he didn't do unsettling killings in the prequels. He wiped out an entire tribe including the children before he married Padme. He told her what he did and this was years before he goes to the dark side.
More over people change, Anakin was able to be redeemed by his son even after all the horrible things he did. Han and Lando were both more selfish characters when they hung out prior to the movies. Both start taking on responsibilities for the greater good and changed. In fact Landos' "betrayal" was only for the sake of the city, he received no reward for doing so. When he's talking about what he's trying to do with Cloud City before the Imperial reveal even Han notes how he's changed into a responsible man.
Han himself went from a loner to a respected general that grew in leaps and bounds. While he was already more together than Anakin was in episode 2 in ANH we see how much more mature he is in ROTJ. Anakin clung to a selfish love not willing to let Padme go. In another version (I think it was the novel version?) he was jealous of Obi-Wan and suspected Padme was having an affair with him. Han gets jealous of Luke sure but he's still there when Leia needs him ("hold me") and was willing to walk away to let her be happy.
Having him shoot Greedo first to defend himself--after trying to negotiate his way out--doesn't diminish that. Han Solo has a great character arc where he allows himself to care for others and betters himself. Redemption is a main theme of the original trilogy so even if "murdering" Greedo did paint him in a bad light he would have been a different person by ROTJ.