Can dimethylmercury originate from cleaning up a broken thermometer with disposable wet wipes?
According to the US EPA, disposable wet wipes are a recommended tool for cleaning up a broken CFL. Although having a number of adverse health hazards at high concentration BZK is a common ingredient in many sanitizers, wet wipes and disinfecting wipes, where it occurs at very low concentrations; typically much less than 1%. These ingredients are not likely to react adversely with the released mercury.

For future reference to cleaning up broken CFLs, be sure to read this guide.