I want to host the site on host that only provides a dedicated IP, not a static one.
While there is often a difference (shared hosting vs. dedicated servers), dedicated IPs typically are effectively static (i.e the point is to provide a stable public IP).
The managers of one.com will not set a DNS record to send example.one.com to the hosts' Nameserver, but will point to the IP address.
The managers of one.com sound like they are handling the DNS for example.one.com.
Since this IP can change, I am worried about possible surprise downtime.
As @JakeGould points out, if you are truly worried about this, you need a (likely more expensive) plan with a dedicated server.
I am curious if one of these options might work.
It seems unlikely the first two would be viable for a few reasons. Regardless, they almost certainly wouldn't solve your concerns about downtime anyway unless your were somehow able to involve your hosts nameservers. Nameservers simply point to an IP address as well. So if your IP for your hosting changed, your site would still be down until the nameservers were updated.
Can I still add a subdomain under example.one.com if I'm only pointing to an IP?
Probably not. This has nothing to do with pointing to an IP. This has to do with what one.com will allow with DNS on their platform. Since example.one.com is already a subdomain, my guess is that one.com will not support sub.example.one.com itself.
Suggestions
Investigate a CDN service such as CloudFlare. Their basic service is free and would potentially help mitigate any downtime (since they duplicate the content of your website).
Get another domain. At a guess, I am assuming example.one.com is free. Domain names often cost less than ~$15/year and having one that isn't controlled by one.com will give you much more freedom (such as assigning nameservers of your choosing).
If you are absolutely desperate not to pay any money, a dot tk domain might be available. Just as a small recommendation, Namecheap FreeDNS is a good free DNS solution if you need one as well.
4“Since this IP can change, I am worried about possible surprise downtime.” Then you need a dedicated plan with a static IP address. No way around that. – JakeGould – 2017-10-11T22:51:21.963