OP, do you think that lawyers have a magic wand on them which means they can 'know' (or, as you put it, 'KNOW') things about people such as guilt? Because surely, if we did, why bother with the expense of a justice system? it would save so much time and money if lawyers could simply determine guilt after a chat with their client. If you can sense for even a second just how horrifically flawed a system that would be, perhaps you will understand why no lawyer worth their salt would seek to influence an outcome in the way you are suggesting they might do.
In reality, lawyers weren't at the alleged crime scene any more than the judge or jury. Which is why the standard to find someone guilty in the criminal courts is not 'knowing' they are guilty but coming to the conclusion that they committed the crime 'beyond reasonable doubt'.
If a client says that they've committed a crime then you can only represent them on a not guilty plea by arguing that the prosecution have not proved the case beyond reasonable doubt. You cannot actively put forward a case saying that they didn't do it if they've told you that they have done it. I also want to correct any impression that a conference between someone accused of a crime and their lawyer is a confessional. It is not. It is a legal meeting where you take instructions and provide advice on the evidence you have before you.
I do not judge my clients because it's not my job to judge them or to 'know' anything about them apart from what is relevant to their case. I treat my clients with respect because I'm a professional not an immature teenager with an inchoate, reductionist sense of morality. Of course I don't like all of them but I recognise that easy assumptions about other people's lives simply don't hold up. Life is complicated; people are complicated. Nice people can do terrible things and nasty people aren't always guilty of everything they're accused of. Almost everyone I have ever met professionally or socially has done something at some point in their life which could constitute a crime, so I think it's really important that we don't try to pretend that there's one type of person who commits crimes and one type of person who doesn't. The reality of our country is that justice isn't blind and only some people get prosecuted for crimes which many types of people commit.
But to answer the original op. No, if I successfully defend a client I do not feel any sense of guilt whatsoever. I haven't done anything wrong so why would I? I'm a highly skilled professional who will have done a difficult job well. There have been occasions when I regret that the case hasn't been properly prosecuted; and there are many times I've disagreed with the conclusion the jury has reached but I'm not responsible for their decisions or how other people do their jobs. I'm responsible for myself and the job I do, the role I play within the system. The best thing I can do for the health of the justice system is do my job excellently, which is what I do do.
So, in summary, the titillating moral quandary you proffer doesn't exist; and if you had subjected it to any or any meaningful scrutiny for even as much as 30 seconds before you pressed 'post' you could have easily worked that out for yourself.