You might try using Google. Enter "site: www.wikitree.com DNA [kit number]" (without the quotes) where [kit number] includes the testing service, e.g., FTDNA-##. That works for me for finding profiles with my own kit number attached, and it includes all the ancestors that have the number attached as well. So it may be a long list, but any of the ancestor profiles should tell you whose kit it is.
Perhaps somebody else will have a better idea.