Thanks. A lot of homebrewers are cold crashing with success and without mediating for dissolved O2. As I said earlier, perhaps if the cold crash is kept short there may not be time for much O2 to dissolve and it takes some time for the effects of oxygenation to affect the beer. That said, I like to
cold condition for extended periods (4 - 6 weeks) and age in the bottle a couple of more months. I brew Belgian Strong Pales.
My process is complex: As the primary fermentation is ~1.005 above the expected FG, I transfer to a secondary. After a couple of days I begin to bring down the temp by 1-2 degrees per day. The idea is to keep the yeast active. Now perhaps Belgian yeast are better at this than the higher flocculating strains but my yeasts will continue to ferment all the way down to 40F (I also use extremely healthy yeast). The fermentation keeps out O2 as CO2 is being produced. I monitor the airlock as the temp is reduced to make sure the yeast are active (airlock activity in a cooling beer is indicative of fermentation). Some days the temp can't be reduce. Once the temp has reached 40F the beer can remain at that temp for as long as I can stand it. This method is not really "cold crashing" so I call it cold conditioning.
You probably don't want to go the this extreme and there are other methods. For your conical, positive CO2 pressure will work great. Commercial breweries that cold crash do this in their bright tank. For carboys, some homebrewers claim success by placing a balloon over the mouth of the carboy as the fermentation nears completion. The balloon fills with CO2 and as the beer is cooled the CO2 is forced back into the carboy. While many disagree, I have been convinced that the "CO2 blanket" is partially a myth and will not protect beer from the relatively large amount of O2 that enters an unprotected fermenter during cold crashing. Here is a link to a thread and a vidio that convinced me:
https://www.homebrewtalk.com/f128/physical-concerns-regarding-cold-crashing-494163/index3.html (post #22)