I don't have access to ssh on my
How is it possible to run composer require(
composer require razorpay/magento) without any cli interface?
It's possible but it is difficult
Essentially you will need a php wrapper
Another option is to composer locally on your machine and upload composer.json, composer.lock and vendor folder.
Try to match php versions
You will need CLI sooner or later so I suggest you sort that out with yor hosting provider ass soon as you can. As far as I know you cannot install modules using composer without CLI. Either way you will need to run
bin/magento setup:upgrade and some other commands to get your new module working anyway.