Well, that's not a cause of death!
If you don't know the reason for the death of the previous colony (was it your colony, or Mark's, or just an old hive passed on by Madge up the road?) it's risky to allow a swarm to take it over
using comb and without cleaning the kit.
If wood, best to scrape and scorch internally and externally. At the very least, scrub with hot washing soda. For poly, submerge in 5:1 bleach for 20 minutes.
Either way, better to have hived on foundation to get them to use honey carried from the previous colony to draw comb to reduce the risk of disease transmission. Comb already drawn will allow them to store the honey for future consumption. EFB in your area is low -
only 6 cases near Bridgend - but better to take precautions.
Main aim when inspecting is to find eggs, after which close up. If none are seen, wait a week and look again. When you have BIAS, look at the advanced open brood and establish that they are uniform, plump, pearly white and curled. If you see any variation, take a photo and post it here.
putting swarms of unknown origin/temperament into a shared area is a bit risky
Good point. A swarm will not reveal its true temper for a while but when the colony is strong you may be unpleasantly surprised and find inspections hard work and uncomfortable. Before you get that far, sense the developing temperament and ask for help to re-queen.
Last year I had five outsider swarms turrn up at an apiary; three were nasty and have been re-queened. The issue is not just for your comfort, but that drones from such colonies spread defensive genes in the surrounding five miles and are a nuisance to other beekeepers.