check the mech to find the specific model number -it should be stamped on one of the link plates – then look up the manual / tech doc for the mech. You need the maximum sprocket size it will accomodate and the capacity – which is how many difference in teeth it can take up the chain slack for. Then subtract the number of teeth on the smallest sprocket from the largest sprocket to get the difference on your cassette * – if the mech capacity is equal or bigger AND the mech will work with the largest sprocket size then you’re in luck, if not then you probably aren’t. You can usually squeeze a few more teeth out of the max sprocket but the capacity isn’t so forgiving.

Is this for a 1×10 setup or a double? My guess would be that a short cage (or medium) will struggle with a 1x setup of a decent range.

9 speed ring and 10 speed chain should be fine but if you are going 1x then you definitely need a N/W ring, chainrings made for shifting do not work well as a single ring as they want to enable the chain to move up or down – e.g. fall off easily. You can use a chain device or a front mech as a makeshift one but its not such a good solution.

* If it’s a 2x or 3x then you need to add the smallest chainring and smallest sprocket teeth then subtract the total from largest chainring + largest sprocket to get the difference, then check it against the mech capacity.