Hm, I think, if you don't want to have scans done, than go with that.
Scans are so inaccurate half the time anyway, and the possible adverse affects, whilst not well documented, do seem to exist.
Sometimes scans do more worry than good anyway.
I know a fair few women who did not have scans and had no problems!
A good midwife will be able to assess you and make sure all is well...I am sure if you would experience any problems, (like bleeding in later pg), you possibly would reconsider anyway.
I did have scan's...and to me the 20-25 week scan felt important, as I have a cleft lip and palate, and whilst it would not have changed attitude and love for the Baby, I felt that I would like to know in advance, so, that I could prepare for it.
I did however, in my last pg refuse Dopplers, and the midwifes used those "trumpet" things (I can't for my life think what they are called), and whilst it meant I "missed" out on hearing my baby's heartbeat, I knew I was doing the best for my Baby, as indeed a midwife will actually be able to hear the Baby's heartbeat much better and will be able to assess better if all is well, as they then hear the real heartbeat, rather then the techno version.
Must admit, I only really found out about the scan/doppler issues when pg with #3.