Can I set my own exchange rate instead of using the live one?

Yes. Go to Settings → Store Settings → Multiple Currencies and untick Auto-update exchange rates from the live provider. Then click Edit on a currency and type your own Exchange Rate (vs default). Keep auto-update off, because when it is on WCart refreshes the rates from the provider on a schedule and replaces what you typed. You can still click Refresh rates now whenever you want the latest rates.