Flying First EWR - LHR on award ticket, then continuing on to CPH.

There are no flights available with miles for LHR - CPH on BA, so considering either:

--Buying Economy ticket on BA (but will it be a total let down after out First flight?)

--Using Star Alliance miles for a Business Class ticket on SAS (which does have availability).

Am wondering if getting luggage, changing terminals is a hassle for the SAS flight, compared to what will be an easy transfer to the BA Econ flight?

Thanks for any advice.