Luigi Mangione‘s legal team’s working to free their client one body part at a time … because they’re now asking a judge to unshackle his hands in the courtroom for future appearances.

According to a letter sent to the judge in the case, Mangione’s side — led by Karen Friedman Agnifilo — is requesting Mangione be allowed to wear court-appropriate clothes instead of a prison jumpsuit, and not have to put on a bulletproof vest.

They also want the restraints taken off his hands … arguing all of the shackles and prison garb unfairly prejudice his ability to get a fair trial.

Mangione’s lawyers say their client isn’t a threat to anyone in the courtroom … claiming he’s been a model prisoner record since he was taken into custody in December.

The lawyers insist the high-profile nature of the case means leaving him in restraints and prison clothing — even during the pretrial phase — could be reported on in the media and could unduly influence potential jurors.

As you know … Mangione was arrested and charged with murder after the December shooting death of UnitedHealthcare CEO Brian Thompson in NYC.