First, I wouldn't cut either of them. I would look to trade one of them for the best draft pick I could get if one has to be cut.
These contracts have made a mess of the Cowboys CAP situation. First of all, look at the position for each of these players. With Gregory and Armstrong both being free agents the Cowboys are in a bind if they cut Lawrence and can't resign Gregory. When Lawrence returned from his injury he did make an impact on the defense. Imagine the defense with Basham and Golston starting.
The same problem exists at WR. Gallup, Wilson, Malik Turner and Noah Brown are all free agents. If you trade or cut Cooper you have CeeDee and Simi Fehoko. If they sign Gallup the situation improves but remember they have to clear $23 million in CAP room just to get under the CAP. I just do not think the Cowboys are going to clear enough space to sign Gallup and Gregory.
If they cut Cooper and Lawrence, they clear $24 million in CAP space. They can restructure both of their contracts and get the same save. But if they do restructure both of them they better plan on cutting them the following year which means finding replacements in the 2022 draft. That means using their top picks on DE and WR when they really need LG and C, and maybe safety if none of their safeties are re-signed.
Based on the way Jerry and his miniMe are talking about Cooper, I think they are going to ask him to take a pay cut. Of course he will say no, as he should. Then they will try to trade him. I think Cooper will get them at most a 3rd round pick from someone. But no one will want Cooper's $20 million salary. So Cooper is staying.
If I was the GM of the Cowboys my plan would be to continue building the defense. Then I would turn the offense into a strong running offense to set up the passing game. That means I would keep Lawrence and re-sign Gregory. I would use the draft to get a LG and possibly a C. I would have Collins competing for the starting LG and RT positions and play the best 5 linemen.
Maybe it is time for the Cowboys to start planning for a rebuild. By the end of 2023 they should plan on dumping all the bloated contracts, Zeke, Cooper, Lawrence, and Dak the following year. Maybe the Cowboys need a purge and a new attitude about the players they draft. This team lacks chemistry. It lacks that winning attitude. I don't think the players are going to change so it may be time for new players.