What's the best way to re-combine the hives? Should I scrape off any swarm cells at this time?
Old bees with queen build foundations and they forget swarming.
The rest bees with brood are not able to swarm. They try to keep brood warm.
New queen emerges and it destroys other queen cells.
You may keep the new queen untill it began to lay eggs, and then you put them together and you kill the old queen. New queen is a good egg maker.
If you have good honey flow, you loose money because it may take 15-20 days untill you can put them together and hive is productive.
It is better after one week kill the old queen, keep hive without queen 24 hours, and then you put parts them together.
But when you need a strong hive, it is better leave egg laying queen and kill the virgin. Old queen lay eggs almost for one generation before new starts egg laying. An that "old" is this year's queen, is it, or under one year old?
Your hive tryes to swarm because hive is tight. You arrage more room and you need not special tricks.