I mentioned using a salvage yard to locate some good condition parts due to the OP stating insurance was not an option. If there is no insurance, then the OP must be on a tight budget to have not had insurance, or does not want to make an insurance claim, perhaps to avoid a loss when selling the car (insurance claim would show up on a car search). This repair will be high, and that's assuming no frame damage (a BIG assumption).
Salvage yards are a decent source to locate parts if on a tight budget. His damage is at the rear; a salvage yard may have vehicles that were totaled due to front end damage, and the rear is clean.
Insurance not being an option is no reason to make a bad situation worse and use parts which can invalidate any warranty on the car. Or result in a sub-par repair.
Not sure why insurance is not an option but if it is because none was present this is going to be one expensive lesson on why one should carry car insurance on any car that one can't just write off in the event of a serious accident.
It is not acceptable behavior to avoid insurance to try to hide the fact the car was in a serious accident. Besides the shop I believe will report the car was repaired and this will show up on the car's record.
But whether the car was in for any accident repair shows up on a CarFax report or not the fact the car was in an accident should be divulged to any prospective buyer. A private buyer but also if the car is traded in. I can remember once or twice when trading in a car to have to sign a document attesting to the fact the car had received no body/paint work. If the car is traded in the presence of accident repair will be obvious the used car/trade in appraiser at the dealer and the lack of disclosure will result in a very low ball offer for the car or even an outright rejection of the car.
'course, to mitigate what effect the history of an accident might have on the car's value the OP should have pics showing the damage both before and after any tear down. And pics of the repairs. And after it is all said and done repair paperwork that shows what parts were replaced, what other repairs were done (paint, etc.) and ideally that factory parts were used.
I'm no warranty expert but it could very well be in this case with the damage where it is the use of salvage suspension parts while it might affect any warranty on that area of the car possibly even the rear end the rest of the drive train and engine warranty and any warranty on other areas of the car should (should) remain in effect.
There is the risk the salvage parts are not as good as they should be. A few times over the years I have been faced with an insurance company trying to bring leverage against the body shop to use used/salvaged parts. To the credit of the shop I had selected in every case the shop recognized the used/salvaged part was in worse condition than the part it was supposed to replace and refused to use it. New parts were ordered and used.
Regardless, if the OP has to repair the car on a budget, even at the risk to any warranty, well he has to.
So yeah, of course, the OP can request the body shop/repair shop use used/salvaged parts. If the OP has picked the right shop it will recognize which used/salvaged parts are ok and which should not be used. There is the possibility there will be no acceptable used/salvaged parts available and to move the car along new parts might have to be used. So the OP has to be ready to accept that possibility.