Try connecting your trainer (and HRM) via the companion app (Bluetooth) on your phone and continue to run Zwift on your laptop. Start companion app, switch on your trainer then start Zwift on your laptop. It's how I run mine and (touch wood) never had an issue.
From Janine, Unfortunately I have had to make the decision to scratch. My left hand has become completely numb and I can't grip the handlebars anymore. It's the same side where I damaged the nerve last year so not worth risking further damage. Disappointed but I would rather have a working hand.