You're good to go... most likely:
There are decisions based on FAR 91.213 (d) that would have to be answered first but if you run down those, odds are favorable that you will find that you can legally de-activate or remove the shoulder harness in an airworthy manner.
To be considered airworthy your aircraft must meet its FAA approved type design or be in a properly altered state. That means everything installed must work or be altered "properly".
So how would you "properly" alter your Piper with the shoulder harness issue?
FAR 91.213 (d) allows you to fly with inoperative instruments or equipment.
(d) Except for operations conducted in accordance with paragraph (a)
or (c) of this section, a person may takeoff an aircraft in operations
conducted under this part with inoperative instruments and equipment
without an approved Minimum Equipment List provided—
(1) The flight operation is conducted in a—
(i) Rotorcraft, non-turbine-powered airplane, glider, lighter-than-air
aircraft, powered parachute, or weight-shift-control aircraft, for
which a master minimum equipment list has not been developed; or
(ii) Small rotorcraft, nonturbine-powered small airplane, glider, or
lighter-than-air aircraft for which a Master Minimum Equipment List
has been developed; and
OK, your piper clears #1.
(2) The inoperative instruments and equipment are not—
(i) Part of the VFR-day type certification instruments and equipment
prescribed in the applicable airworthiness regulations under which the
aircraft was type certificated;
Your Piper was certificated under CAR3... just try to find anything about shoulder harnesses there... So far so good...
(ii) Indicated as required on the aircraft's equipment list, or on the
Kinds of Operations Equipment List for the kind of flight operation
Read through your AFM or POH to see if it requires it. Maybe it does but I doubt it.
(iii) Required by §91.205 or any other rule of this part for the
specific kind of flight operation being conducted; or
91.205 requires lap belt only (metal type) but does not mention shoulder harness. I'm assuming the shoulder harness is not an integral part of the lap belt. This is key... you need a lap belt.
(iv) Required to be operational by an airworthiness directive; and
Been doing this my whole career and I'm not aware of an AD about it that is applicable to your aircraft.
(3) The inoperative instruments and equipment are—
(i) Removed from the aircraft, the cockpit control placarded, and the
maintenance recorded in accordance with §43.9 of this chapter; or
(ii) Deactivated and placarded “Inoperative.” If deactivation of the
inoperative instrument or equipment involves maintenance, it must be
accomplished and recorded in accordance with part 43 of this chapter;
Ok, you need to have an A&P remove or deactivate it, write a maintenance entry about removing it and placard it as "inop" if necessary.
(4) A determination is made by a pilot, who is certificated and
appropriately rated under part 61 of this chapter, or by a person, who
is certificated and appropriately rated to perform maintenance on the
aircraft, that the inoperative instrument or equipment does not
constitute a hazard to the aircraft.
Well, it could constitute a risk to the occupant I suppose, but not a hazard to the aircraft.
An aircraft with inoperative instruments or equipment as provided in
paragraph (d) of this section is considered to be in a properly
altered condition acceptable to the Administrator.
That's how you properly alter your shoulder harness issue to a manner acceptable to the FAA...