If two instruments were ever meant to be together, it's uke and kazoo. Both are derided as novelty instruments but are fun and accessible. Kazoos have that 'brass on a budget' sound which go great with the ukulele. They also bear a resemblance to
Ukulele Ike's distinctive scat singing. Judging by the clips on YouTube, they seem to be the clear choice of secondary instrument for ukulele players.