Yes as long as they are 8 speed.

Well, you get what you pay for. The only visible difference is that 8.93 has silvery sideplates and grey inner links while 8.99 is all silvery. Unsure if this translates to greater durability or is purely cosmetic. However, both of them will certainly work with the HG40 cassette which is of middling quality in Shimano's range. The difference between HG30 and HG 80 is in material, construction, surface finish and weight. All deraiileur chains for any number of speeds are 3/32inch between outer plates with the exception of one failed Shimano experiment in 10 speed Dura Ace chain. All chains for 6/7/8 speed are around 7.1mm measured across the link pins while 9 speed chains are around 6.5mm on account of the narrower cog spacing in the 9 speed cassette.The 9 speed chains achieve the narrowness with thinner outer plates and shorter pins. Trust the chain manufacturer. If it's a reputable name and it's marked 8 speed it will work with a 6/7/8 speed cassette.

If you use the search option and search for "7 speed chains" you should get three suitable results.

Any 1/2" x 3/32" 8 speed chain should work fine with the Nexus system so the X8-93 should be good for you.