You should not need to download any of their software to pay a BitPay invoice. However, they may try to force you to sign up for an account and verify your identity with KYC before you are allowed to pay, which is utterly ridiculous, but that's how BitPay works. Once they show you the QR code, you should either be able to scan it with your wallet, or click the copy button to display a raw address and amount which you can then copy in to your wallet to pay the invoice.
Who is the merchant in question? Can you find an alternative which does not use BitPay? Or maybe buy a giftcard with your bitcoin which you can spend with the merchant, therefore completely avoiding BitPay?