These small panels do not have a "main" breaker at the top of them like larger panels, instead, they use a backfed breaker (which by code must be retained in the panel/stabs, by a special, approved clip or bracket to prevent its removal) as a main breaker. I do not see any lugs on the ends of the buss's, however, if there are lugs on the buss that do not show in the pictures, you could simply do away with the main breaker, if it is, as you say, adjacent to your existing panel, which has a breaker feeding the 125 amp sub panel.
If you have knockouts on the front panel for the two positions you want to mount the 240V breaker in, and the instruction placard on the inside of the cover (if there is one) doesn't have any restrictions, I see no reason to not use the space.
You should clearly label the main as a main breaker, and I do not see a retaining clip on it (but it might be out of view) and if there is not one, I would look into purchasing one. This is required by NEC 230.70(B).
Charles