I would try BCV (Banque Cantonale Vaudoise). They are based in Lausanne but have branches all over the canton including in Vevey. A friend who has a small business has used them for the past 5 years and speaks highly of them. I have banked with them for a year as an individual and am pleased with the service. Most of the people I have reached on the phone will happily speak English if you prefer.