Google pictures suggest that hub has a Hyperglide (HG) hub. It is kind of standard since 95% of all bikes have that. both SRAM and Shimano make cassettes for that (as do other manufacturers like sunrace etc.).
If you look up the exact cassette number, you see what it is, but if you have hub and cassette in hand, you should be able to fit if it fits...
HG hub has an 11T minimum cog size.
You need to turn the cogs or spider in the right degree in relation to the hub splines. All the splines are different in width and distance to each other. The cassette only will fit one way unlike a crank for example. This is to make sure the shift ramps on the cogs are in proper relation to each other. Look at the teeth, some look like worn or oddly shaped, there is a reason for that to improve shifting.
If by new shimano hub you mean their newly released 11 and 12-speed, this isn't really available yet (Microspline) . But that will be a different shape. Same way SRAM had some new hub (xD). both of those new hubs support 10T cogs and are not compatible to each other or to HG hubs and cassettes.