B737-800 Captain reported a fume event during cruise caused by a leak of a cockpit fire bottle. After completing appropriate QRH procedures flight continued to destination and executed a safe landing.

Narrative

FL360 Crew heard a Pop then hissing. CA (Captain) determined Fire Extinguisher was discharging under the Bottle pressure gage; however; nothing visible; no odor or irritants; only cool sensation on fingertip below gage. CA immediately had crew don O2 masks and establish crew comms per QRH. FO (First Officer) given PF (Pilot Flying) as CA entered QRH at Smoke Fumes. This Checklist focused on Fire for Electric or Bleed Air; with NO sight; smell; odor checklist ended step 14. CA restarted same checklist and selected Toxic substance which led to new Checklist. However; decision tree led to Toxic Gas; Not in Cabin; which led to notify FAs and then Dispatch and finally Maint. CA concerns were Toxic Gas thru FD deck door grill to FA 1 (Flight Attendant) and guidance on Halon removal time for Flt Deck. The Bottle gage needle stopped below Green Zone and then held w/ no sensation or coolness. Maint said no guidance existed for Flt Deck Air quality after Halon discharge. Best guess was 15 mins (PBE Limits?). Crew waited 20 mins removed O2 masks and noted no symptoms and continued. Fire Bottle Gage location can increase bumping bags or bodies into it. NO guidance at [company] on toxicity of Halon nor training. Crew was expecting some visible indication. Halon Fire Bottle usage only mentioned in QRH under Lithium Ion Battery Overheat. No info available in FOM on Halon Discharge; only HAZMAT. Crew was lucky Entire Fire Ext Bottle did not discharge. Maintenance Techs discharged remaining contents of bottle outside - crew only noticed slight fog from gas pressure release; but no color; odor or sensation. Better information and training on Halon toxicity and usage on the Flight Deck vs Cabin. Would Noise Cancelling headsets block the hissing sound of Halon discharge? I use Telex 850 passive headset and heard this sound. Recent QRH update mentions rewording of Fire Extinguisher contents...