FAR 91.211 only requires supplemental oxygen be used by the pilot/minimum required flight crew for that part of the flight at altitudes above 12,500 MSL to 14,000 MSL that is of more than 30 minutes duration.
There is no regulatory requirement that all aircraft with a service ceiling above 12,500 MSL are required to have oxygen aboard (although it is an important safety consideration and should always be available if needed even at lower altitudes).
If ATC assigns (by way of a clearance or instruction) an altitude that you believe may be unacceptable/unsafe for any reason, you can tell them that you are "unable" and can ask for a different altitude assignment. If a different altitude is not available for assignment and you are VMC you can always cancel IFR and continue the flight under VFR (with advisories). If you are IMC and need to continue IFR you can ask for an alternative route or other option that may be available in order to maintain an altitude that meets your safety needs.
However, as the Pilot-in-Command (PIC), you will never be required by regulation to operate contrary to your assessment of what is safe. FAR 91.3 - Responsibility and authority of the pilot in command states (in pertinent part):
(a) The pilot in command of an aircraft is directly responsible for, and is the final authority as to, the operation of that aircraft.
Also, it may be helpful to review (in concert with FAR 91.3), FAR 91.123- Compliance with ATC clearances and instructions. This regulation specifies your obligation as a PIC to comply with an ATC clearance or instruction as well as the circumstances that allow for deviations from, or operations contrary to, an ATC clearance or instruction.