Unfortunately, it is impossible to use a certificate on any server without the private key. Anyone on the Internet can find and download your certificate if they wanted, as it is necessary for them to securely transmit data to your server. It is the private key that enables you to negotiate connections with and securely transmit data to clients on the Internet.
If your hosting provider does not make the private key available to you, the best option for you in this situation would be to engage your web hosting provider’s support about setting up their web server to proxy your websockets for you. (It might be as easy as dropping an
.htaccess file in your web directory, but only they would know whether they support this or not.)
Otherwise, you would have to create a new certificate that you do have the private key for to use for this purpose, which is difficult to do with Let’s Encrypt without shell access to the server.
So, if your webhost is unwilling or unable to make the private key accessible or set up their web server to proxy websockets, you would either need to purchase a certificate from a commercial CA or seek out a more flexible hosting provider.