It is extremely difficult to make an exhaustive list of ALL older noble families of Sweden.
There are a few things that should be understood about medieval Swedish nobility:
(1) in many earlier cases, any royal letters-patent (sköldebrev) were never actually issued. This is approximately the phenomenon of ancient or original nobility, uradel. Actually, most of really old svenska frälsesläkter got their noble position by establishing it themselves, and generally without written record. The crown just RECOGNIZED them nobles in subsequent events (quite often by remaining silent and just treating them as nobles, according them those privileges). And, they had their Coat-of-Arms by just assuming such by themselves, for tournaments and warfare signs. Only some such families later had some explicit royal confirmation (such as sort of registation of their Coat-of-Arms).
(2) Even starting from about the early 15th century, when kings rather regularly issued explicit ennoblings, all such documents are not preserved, or their former existence known to us.
(3) Some documents are dependent on interpretation: whether it actually constitutes rank of nobility, or is some other privilege. For example, there were a bunch of families bordering lower nobility, to whom kings, or castellans or great officers of kingdom, acting in name of monarch, recognized exemption from taxes, or somesuch privileges, which has been construed by some (at least beneficers themselves) to signify nobility - and vociferously denied by some others. Some literature tends to call those knapar. (Actually, in first decades of Riddarhuset's existence, several families got introduced with less than satisfactory proofs of full nobility, if our current källkritiska standards were observed.)
(4) if you limit your desire to those who are undeniably noble (by the way, how to decide that?), for example desiring a full collection of families of riksråd and/or riddare, then a problem exists yet: we do not know precisely genealogies of all of them. How to make a clear and full list of noble houses, hen you cannot be sure whether this or that riddare or riksråd actually were an agnate of this or that family.