my aim with the engineer is better than it is with the scout because you can't go jumping crazily and you are slower. Also the widowmaker is just too awesome and I recommend improving your aim just for that gun. that said if your aim is rubbish you need to work on that but there are a couple of things you can do on 1 vs 1.

Vs soldier: I play 5CP more than I do other modes, so unless I am setting up big sentry defense on last I run the gunslinger. Vs soldier, I plop down a mini and let it shoot the soldier while I short circuit all his rockets.

vs sniper: absolutely nothing you can do vs one unless you caught him unaware from behind. which won't happen if he has a team that supports him and a sentry up his butt.

vs medic: you shouldn't be losing to a medic.you have hitscan he has a high damage needle gun that you can dodge or a high damage arrow that you can dodge. he runs faster than you, but as I said, you have a hitscan weapon. beware of the ubersaw though. it has the range of the eyelander and crits like pan. And some medics are very good with using the needleguns (the xbow works really similar to the huntsman, we're lucky it can't headshot. needleguns hurt too but most medics never practice and get to know the arc).

vs. demo: same as medic, it's easy enough to dodge pills and hitscan is faster. be aware that midrange is his domain, up close he can't do much unless he uses melee , ranged you can pepper him with pistol if you run that. Also? the short circuit + mini. same as soldier.

pyro: if you caught in an airblast, nothing you can do. otherwise just shotgun him - a lot of them run flare/detonator. otherwise it is shotgun vs shotgun and whose aim is better. unless they catch you in flames, you can shoot them still but they have the health advantage.

scout: a good scout will destroy you. you are a slower version of them. BUT you have the mini which gives you a chance.

heavy: honestly? you aren't the right class to approach a heavy. sure you can surprise them from behind, but a well aware heavy>you.