3rd party shop's labor rates will almost always be way lower than the stealerships, however, if you go this route, a few things to be aware of:
A) Call the shop(s) first to be certain they are ok with you supplying the parts. Some places are, some are not...And most of them will tell you right up front that they obviously won't offer any warranty on the parts, just the work/labor. But if you buy OEM parts that should not be an issue...
B) Make 1000% certain that you absolutely have the correct hoses & all the clamps/fittings ect.... or else you may see the dreaded "Misc shop supplies" charge on your bill..which will probably be there to compensate for them not being able to mark-up the parts, and be sure to ask for an explanation of what those supplies were..
C) They may raise their labor rates a little from a job where they source the parts, again to make up for the lack of mark-up on the parts you provided. Getting a detailed, written estimate will usually make it clear what the rate is going to be from the start.
D) Be sure to tell them that you want the old parts returned to you (and if there is a checkbox is on the work order, put a check mark next to it) as some shady places will just remove & then replace the old parts to make it look like they did the work and installed new ones when in fact they just did a switcheroo on you...
I have a trusted shop near me that I have been dealing with for almost 20 years, and they are happy as loonies when I bring the parts, as it saves them time & effort and allows them to finish the job faster, which in turn allows them to do more work each day.... a win-win in my book....