I'd stick with the AFTER trigger. Your initial trigger was pretty much spot on.

In case you create other AFTER triggers later, you might want to explicitly designate that trigger as the first (or last) one to fire after an INSERT/UPDATE:

EXEC sp_settriggerorder @triggername = 'dbo.tr_Cust_insupd',

@order = 'FIRST', @stmttype = 'INSERT'

EXEC sp_settriggerorder @triggername = 'dbo.tr_Cust_insupd',

@order = 'FIRST', @stmttype = 'UPDATE'