Waves to girl having to wheel herself along (6-5)

I believe the answer is:

roller-skate

'to wheel herself along' is the definition.
(to roller-skate is to move on wheeled shoes)

'waves to girl' is the wordplay.
'waves' becomes 'rollers' (roller is a kind of wave).
'to girl' becomes 'kate' (girl's name).
'rollers'+'kate'='ROLLER-SKATE'

'having' is the link.

(Another definition for roller-skate that I've seen is " travel through revolution?".)

I've seen this clue in The Guardian.

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