Adding Key Lock mechanism to door with tubular mortice latch

I want to fit a key lock mechanism to a door, ideally want to fit the key lock mechanism without changing the door too much and since the door already uses a tubular mortice latch the solution I reached to is to use a keyed lock door knob or lever handle, example [  https://www.amazon.co.uk/Qrity-Stainless-Entracne-Passage-Lockset/dp/B06XKJHDP6 ].

Pic of the door without the spindle of the tubular mortice latch, the latch seems to be similar to this https://www.screwfix.com/p/smith-locke-chrome-tubular-mortice-latch-64mm-case-45mm-backset/339px and has the same 45mm backset so I won't be using the latch they are providing since it has a larger backset but since my current latch also has 2 extra holes like the screwfix latch, that are correct distance apart so it probably will work with the door knob above.

This seems reasonable since this is an interior door and doesn't need to be that strong and would fit criteria of not changing the door too much. But I don't know much about locks and such so want to know if anyone else has experience dealing with these kind of key lock door knobs or levers from amazon that work with tubular mortice latch.