Let's deconstruct that.
The song only mentions India as being where the tigers are. There's no mention in the lyrics of the Indian people or culture.
Other than that, we have a novelty song by British songwriters about tigers and hunters. Lyrics expressing concern about things like table manners suggest that the hunters are British. To me, the songwriters are pitting stuffy men in pith helmets and jodhpurs against tigers, who have the hunters overmatched. These images obviously evoke British colonialism, which isn't a surprise because the song
was written during the British colonial period. The song was written around 1930 (I couldn't find the exact date), and India didn't gain its independence until 1947. The song was written by the British songwriting team of Evans, Damerell, and Hargreaves, who also wrote "Lady of Spain" and "Let's All Sing Like the Birdies Sing". They also wrote the song pictured below.
The "Watusi" reference was added during the Bonzos' 1960s cover of the song. Watusi is an African word that was used for a dance popular in the 1960s. In general, my memories as a child in the '60s are that entertainers for some reason found it hilarious to use the word Watusi. This eventually ended up in Adam West as Batman doing the "Bat-usi". After that, everyone re-thought the whole thing.
(Aside: Here in Massachusetts, the Mt. Wachusett ski resort uses an advertizing jingle "Wa-Wachusett". I just discovered that this was cribbed from a 1962 pop hit "Wah Watusi".)
When setting out to play this song, my conclusion was that the song is less politically incorrect than some standards of the ukulele repertoire like, say, "Ukulele Lady". I was more concerned that the lyrics are too dated. For instance, will ukulele players of today know that "fretwork" as used here means "dentures" and not musical instruments?