Reading through it, that situation doesn't appear to be specifically addressed, but I _suspect_ that it would depend on the specifics of the case:
* If you are suing an LLP, you are taking an action against an individual member of the partnership, thus they can appear as the defendant. Though 12.40.080 can be read as excluding attorneys regardless of their status as the defendant, I believe that has to be read in conjunction with the notice that the court issues under 12.40.060. The defendant is "direct[ed] and requir[ed ...]to appear personally in the small claims department", thus granting the permission described in 12.40.080(1). Even if that is not the case, it would seem inequitable to prevent the defendant appearing, thus I would expect the judge to grant permission to appear.
* If you are suing a larger company that ISN'T operating as an LLP, it would seem likely that they would have staff beyond the attorneys/legal paraprofessionals, thus they can represent the company.
* If you are suing a corporation that is truly made up of 100% legal professionals, that seems to be the case where things get somewhat murky, though that really does appear to be a corner case. The restriction in 12.40.080 is quite clear: "A corporation may not be represented by an attorney-at-law or legal paraprofessional", and I suspect it gets into the minutia of interpretation that I am not equipped to determine. However, I do note that 12.40.060 requires the defendant to appear, not _necessarily_ participate in the hearing. Thus, perhaps the hearing can proceed WITHOUT representation from the defendant, allowing the judge various options to achieve a equitable result (transfer the case to the district court where the restriction is lifted, issue a judgement if the facts are clear or it seems the company setup is deliberate in order to try and avoid the small claims court, summon employees as witnesses -- so even though they are not representing the company the facts of the claim can be established, make an order permitting a legal professional to represent the company--depends on the extent of judicial powers/making an equitable case to overrule the restriction etc.).
Note that this is just based on reading through the linked laws, and is likely wrong/inaccurate in some ways. However, it does appear that a law firm would have options beyond a default judgement.