It's up to the prosecutor as to what charges will be brought against you. Being open and honest could implicate you with even more charges. The best policy is to say nothing.
This is an advice a lawyer will give you, simply because the evidence against you is too overwhelming, and fighting for your innocence will most likely result in a harsher sentence.
Your assumption is that you will know the final outcome of the consequences. There is no way to fully know the future repercussions of admitting to a crime which you did not commit. Since committing a crime is a known negative value, the rational course would be to not confess to a false charge.