Hi,
Well, there is no particular thing to change for SMTP in HikaShop.
However, since you're using another method to send the emails, it might have other requirements.
For example, if you include a PDF invoice in the emails, maybe the SMTP server doesn't like that.
Or maybe the enconding format of the emails needs to be changed. It's hard to say without looking at the error in the log of the email server. That's why contact the hosting support is what I recommend. You already know that HikaShop do send the emails to the email server, so it means that the email server doesn't send them for some reason and the reason will be in the log of the email server.