Install certificate using OpenSSL?

Hi there, I have a slightly confusing conundrum that I'm hoping to get some advice on. This is technically outside of my comfort zone, so I apologise in advance if this question comes across as a little 'muddy', but I'll try to phrase it as succinctly as possible. I'm required to install an SSL certificate on our server in order to authenticate communications between our site and a third-party service using their API. I have no doubt that the third-party are a trustworthy company - we've used them for years. I'm not 100% sure that they're very familiar with cPanel servers, however, so I don't want to blindly assume that their advice is suitable for our setup. The SSL certificate I've been requested to install is generated by the third-party company, after I sent them our CSR generated from within cPanel. Unfortunately, the generated certificate will not install using cPanel or WHM's SSL interface, failing with the message; "error Certificate verification failed! The system did not find the Certificate Authority Bundle that matches this certificate. Contact "Third Party Company." to obtain the Certificate Authority Bundle for "ThirdPartyCompanyCA"." The company can't provide me with a CA Bundle and would instead prefer that I attempt to install the SSL certificate directly onto the server using something like OpenSSL, bypassing cPanel/WHM altogether. My question is, quite simply, is this advisable? Generally, I try not to bypass cPanel/WHM for anything unless absolutely required - but I'm hoping that someone here can advise me whether installation of an SSL certificate in this manner is safe/appropriate for a cPanel/WHM server. Again, we can assume that the third party company is trustworthy - but with all the best intentions in the world, I don't want to assume that their advice is correct. Thanks in advance for any thoughts.