From the liner notes supplied with an EMI recordings release, performed from 1968-71, digitally remastered in 1998, and compiled in 2007...
With Simon Preston as organist and the Menuhin Festival Orchestra conducted by Yehudi Menuhin...
Concertos 1, 5, 13 & 14 Merchant Taylor's Hall, London
Concertos 2, 3, 9 & 15 Great Packington Church, Warwickshire
Concertos 4, 6, 8 & 10 Queen Elizabeth Hall, London
Concertos 7, 11, & 12 St Paul's Girls' School, London
We normally associate organ music with the church, and with large, powerful instruments which produce a thrilling variety of sounds. But Handel's organ concertos were actually composed for the Theatre, and were intended for small, portable English organs which had a light, delicate tone, and were provided with just a handful of stops, but no pedals. Handel's concertos were deliberately popular in character, and were designed to entertain audiences during the intervals of his choral works and oratorios.
I hope in listing the locations where this relatively "new" set of recordings was made along with the description quoted above this will give you some insight...
Seems a "barrel organ" would be an ideal instrument to reproduce the "organ" portion of the concerto as these would likely contain the appropriate stops... However...
Handel's improvisation did not stop with the introductory "voluntary movement". In later life, after he had become blind, he tended to avoid playing his earlier concertos from memory, and according to one eyewitnhess he chose instead to 'trust to his inventive powers... giving the band only the skeleton, or ritornels of each movement, he played all of the solo part extempore, while the other instruments left him, ad libitum, waiting for the signal of a shake, befrore they played such fragments of music as they found in their books.
The published versions of Handel's later organ concertos bear this out. In the Concerto in D minor (Op.7 no.4), for instance, the second movement contains a total of six "ad libitum" markings for the soloist which actually require the improvisation of whole passages in
continuation of ideas suggested by the composer. Thus no two performances of the concerto should ever sound exactly the same, especially since the third movement is left entirely to the discretion of the performer.