Well it depends at what point he outlined he wouldnt want to join. If it was in chapter 1 where he defends the upper class girl they most likely would have left him but if it was in chapter 2, he would've been put to work in a factory as najenda said or killed if he still refused. So for this I am going to assume he says he wont in chapter 1. After seeing his childhood friends killed, he would still kill the girl but akame would then leave him as he wasnt a target. From this he would likely move into the imperial military and since he saw the members of night raid, they wouldnt be able to operate in the capital as all of the members would then have a wanted poster (Apart from chelsea and susanoo but they come in later). From this we can also assume that he would be given a teigu for his strength, this may be incursio as tatsumi wouldnt be there to fight the three beasts and return to Night Raid. He would develop his powers like before and would probably be invited to the Jaegers in which Esdeath would do her thing again. Throughout all of this, major events wouldnt happen such as Tatsumi's attempted execution and how he saved Mine so we can assume That Mine, Lubbock, Chelsea, Bulat, Sheele would be dead before the final battle. As Tatsumi wouldn't fall in love with Mine he would likely have to fall in love with Esdeath and since he would have no need to fight Shikoutazer Night Raid would have a large battle against the Jaegers with Najenda, Susanoo, Leone and Akame against Wave, Kurome, Tatsumi, Esdeath and Seryu fighting against each other. It is likely that Susanoo would die, redering najenda useless and Leone dying. On the jaegers kurome would probably die and seryu would probably sacrifice herself for 'justice'. This would leave akame vs the rest of the jaegers and Shikoutazer would not have been destroyed as tatsumi isnt going to stop it. Akame would then die and the Jaegers would win, allowing the pain of the kingdom to continue. (Oh and little Esdeath and Tatsumi children would be around)
This is just my ideas, hope this helps
-R