How Many Clients Could Not Send to Bech32 Addresses?
As an answer didn't appear to be forthcoming, I did my own research in order to address this question.
Based on the information provided by the Bitcoin Wiki on Bech32 adoption, I surmised the following information.

All mainstream software wallets support sending to Bech32.
All mainstream hardware wallets support sending to Bech32 (either directly or via Electrum).
All major web wallets support sending to Bech32.
Most exchanges support sending to Bech32 (although notably Bitrex and LBC don't).

Note that I have specified sending because a lot of these do not support receiving funds via a Bech32 address as of yet.  However, for my particular requirement that is unimportant as it is about sending only.
With the above facts confirmed, the answer I actually gave to my client was:
Nearly all wallets can send to bech32 including most commercial wallet providers so you don't need to worry.
When he asked what percentage, I was unable to answer it.  I would need to know what percentage of daily volume went through the exchanges that didn't support Bech32.  However, given then pretty much every wallet does support it I felt that this was less relevant.