61.37 Recent flight experience
(i) If the holder of a pilot licence issued in accordance with this Part has
not met the requirements of rule 61.39 for a period of 5 years or more, the
privileges of that pilot licence may not be exercised again unless...
61.39 Biennial flight review
(a) Except as provided in paragraph (b), the holder of a pilot licence
issued by the Director under the Act and this Part must not exercise the
privileges of the pilot licence for longer than 24 months from the date of the
issue flight test for the pilot licence...
(c) A biennial flight review must—
(1) be conducted by an appropriately qualified flight instructor; and
(2) consist of flight instruction to review those manoeuvres and
procedures applicable to the pilot licence privileges the holder
wishes to exercise
61.41 Use of lower pilot licence or rating
(b) The holder of a pilot licence issued in accordance with this Part who
does not meet the currency requirements of rule 61.207 (CPL) or rule 61.257
(ATPL) for the pilot licence type, but who meets the currency requirements
for a lower pilot licence, may exercise the privileges of the lower pilot licence.
You could be ok. The five year clock starts from when you were last due a BFR. If you got the license (or passed a BFR) six years ago, you don't need to resit the law exam - it's only been four years (starting 24 months after the last BFR) since the licence went un-current.
Assuming you do actually need to do a law exam...
There is nothing in Part 61 that says you have to maintain the highest grade of license you hold. Remember that you hold a PPL as well as a CPL. As 61.39 and 61.41 clearly say, you the pilot get to choose which level of license you wish to maintain!
With that in mind, it is perfectly acceptable for a CPL holder to do a PPL BFR, and retain only PPL privileges. It's not unheard of, and the log book sticker will clearly say "PPL BFR".
I would advise you to do the law exam that you need. With an expired CPL in your hand and a fresh PPL law exam, an instructor will have no problem conducting a PPL BFR with you, with you retaining only PPL privileges.
For peace of mind, perhaps you should consider contacting the CFI of the aero club you will be using, to ask whether he objects to conducting a PPL BFR on you, if you hold a fresh PPL law pass. Mention that you're seeking confirmation of rules 61.39 and 61.41.
Best of luck,
O8