I would answer that the addition of a stirrer in the production of Colloidal Silver would be beneficial for all but the air pump solutions. - based on what limited effect these have as well as the introduction of air(enrichment) into the solution(aeration). Which in turn, undermines the purpose of using purified water.
That said, I'd also add that there are widespread misconceptions from sellers on the use of polarity reversing circuits. To which I'd add, actually promotes the liberation of silver oxides in solution rather than stopping it.
And so here again, the advantage goes to the fixed polarity circuit, in that the oxides collected on the cathode(s) can potentially be removed rather than released into the solution.
That said, and with respect to the formation of oxides, the misconception here is that the use of polarity reversal would somehow avert the electrolytic principals used in the production of Colloidal Silver . - to which I'd add, nothing could be further from the truth.
Hope this helps
PS. there are very affordable magnetic stirrers(less than 30 USD) that can be purchased on eBay that would work for most DYI CS generators.