Intel's factory cooler on the i5-8400 was considered inadequate, allowing/causing near throttle conditions under heavy loads, exactly as you describe. (Safe to assume the tradition continued with the i5-9400's 100 MHz jump in clock speeds)
(If your case is not small, the Scythe Mugen 5 air cooler is about $40-$45...)
Since you intend to knock off .05V core voltage and/or perhaps knock 100 MHz off the peak all core turbo, I'd see if Intel's XTU will allow you to implement a few tweaks to keep temps down to 84C or less..