Board Thread:The Reference Desk/@comment-1292820-20140123070106/@comment-24894325-20170526220930

If the dates of birth/death of John Brandon in IMDB are compared to the information from this obituary, it is almost certain that this is the same person. The obituary puts his birthplace as New York. Thus, he is American.

While it is unlikely that public records could definitively prove someone is the first American actor in Doctor Who, it seems fairly certain that the OP's question can be answered in the negative: Stubby Kaye was not the first American actor.