With hindsight, I'd have replaced the 4.7" with 4" DPs in a heartbeat. Destroyers spent most of the war acting as AAW/ASW escorts for fleets or convoys and the 4"DP was far more use in that role. When they did engage other surface ships, they were usually destroyer-sized or smaller, with negligable armour, so the smaller round of the 4" wouldn't have mattered. As for range, well most destroyer guns over 4" calibre had a ballistic range that exceeded the practical accurate range, given the limitations imposed on their fire-control by low directors and excessive movement in any seaway. Under those circumstances, the higher fire rate of the 4" was probably more useful for getting a hit than the longer range of the 4.7".
Not sure about dumping the Pom-poms though, even with a late-30's mindset. They were there because even the RN was waking up to the idea that short-range AAA was going to matter, so the trend would have been to add more rather than less. The really useless light AAA mounting from that period were things like the quad 0.5" Vickers (not sure if the Tribals had them or not), that just didn't have enough useful range to deter anything before it released it's weapon.