How can allegedly be replaced in a crime situation where the subject has obvious...

A person is caught red handed commiting a crime, but the term allegedly gets used until he has been convicted.

What would be a better word to describe the person so accused?

There's isn't a better term.

The point of using "allegedly" is to hedge against the allegation being wrong and being sued for defamation, which is always possible no matter how "obvious" it seems - note there are legitimate defenses for committing acts that would otherwise be illegal. If you see someone kill someone else, for example, you can allege it was murder, but you might be completely wrong if it was a legal case of self defense. No matter how "obvious" you think the offense is, you have no way of knowing if your allegation is correct until it's tested in a court of law.

In the event the person is found not guilty, having implied their guilt may be a case of defamation. Of course, if you really are absolutely sure of someone's guilt and your ability to prove it, there may not be much need to hedge your language by "alleging" their crimes since the truth is an absolute defense for defamation.

Your choices are to either say that someone claims they committed the crime (they are an alleged criminal), or to say that they committed the crime (they are a criminal). If you're saying the latter, there is no need to qualify the statement at all with a different term. Saying someone is obviously a criminal is no different from saying they are one, which can be problematic if it turns out they're not. You can use any common word you want to describe your level of belief in the person's guilt (a possible criminal, a likely criminal, an obvious criminal, an apparent criminal, simply "a criminal", etc.), but it might be defamatory if incorrect.