You should be fine, though of course all flights can get delayed due to weather and so on.
Sounds like you're flying with SAS from CPH (they operate the BD coded flights), which will arrive in the same terminal and concourse as BMI's transatlantic flights. You will rarely be more than 2 or 3 gates away.
Main thing to remember is NOT to follow the arrivals or immigration signs, but to ask the gate staff for a gate number for ORD, and go to the gate. Provided you have a boarding pass (and you will - SK use the same computer system as BD) you will have no problem doing this. Terminal 1 is not "segregated" i.e. you come off the jetway into the departures concourse, much as with the domestic concourse of a US airport.
To give you some idea of size, T1 at MAN has a gate area smaller than T7 at LAX (similar number of gates, just more compact).
You will NOT need to reclear security (unlike certain airports in London we could mention), though you will likely be subjected to the usual random checks at the gate for the ORD flight.
You will probably have more than enough time (the CPH-MAN flight will have been "padded" so if it operates normally it should arrive 15 minutes or more early). I would feel confident of doing this even with 25 minutes.
Enjoy the flights - both offer very good service indeed!