I would first consider that neither is likely to relieve the patient's respiratory distress, so additional steps will need to be taken anyway to address the dyspnea, but if they're hypoxic then it's generally considered in the realm of a "prudent" nurse to apply oxygen while also initiating the process of notifying the physician.
A sharp increase in CO2 level is more of a driver of dyspnea than hypoxia, with the other main source of dyspnea being a restricted or impaired ventilation; bronchospasm / constriction, pneumo, pulmonary edema, etc.
If this is an acute change where there isn't already a treatment plan in place for this scenario, then this would be when you would initiate a Rapid Response if that's available to you.
When calling the Doc, you should have additional assessment info ready including lung sounds, vitals, LOC, etc. This might indicate prns that are already ordered; are there wheezes? Or worse, were there wheezes and now there's not even enough air moving to make a wheeze?
In terms of the NRB vs Venti, the advantage of the Venti is that you can titrate the oxygen concentration, but if they're hypoxic and/or rapidly dropping sats, then it would make sense to skip the Venti and go straight to the NRB. Keep in mind that the mask, as opposed to the cannula, can potentially work against you. If the sensation of the mask strapped to your face increases the fight-or-flight response, which isn't unusual as a reflexive response to pressure around the nose and mouth, then that can increase the respiratory demand that they already aren't meeting. Or it might feel reassuring and do the opposite.