It's great to hear of another successful wiki implementation.
Regarding your concern about "the tiresome nature of obtaining and managing signatures", there's probably some working solutions to help you here. How are you handling signatures at the moment? Are they electronic? Or do you save a handwritten copy of the document somewhere?
One provision that helped us was to define the minimum level of signing authorities for the various document types. For example a Work Instruction may need a review signature of the author's peer and approval by their manager, whereas a SOP requires department head review and QM approval.
Our system of banners for wiki articles can allow an article to be created as draft, reviewed and approved once complete, with an authorized representative changing the banner to controlled. The article's history record will show who did this and when it was done. By changing the banner to controlled, the authorized representative (document controller or QM rep) is confirming they have witnessed the review and approval by the required authorities. A written record of the review & approval may be kept in some cases, but not many. The records of review are logged in the discussion section of the wiki article by a minute taker and "signed" by the attendees (they add their acceptance by editing the discussion which gets recorded in the wiki's edit history).
Wiki changes don't necessarily need official review. Subsequent drafts will be visible to all, allowing refinements and crowd-sourced corrections to be made as the content matures, under a watchful eye of an owner or other responsible authority (the wiki's watch lists are good for this). If the changes are significant then a new controlled version can be "issued" by re-reviewing the content/changes and obtaining the necessary clearance for approval. The "permanent id" number in the banner is updated and the users are informed of a new controlled version by email or whatever.