Should I send SAT I if I only want Subject Tests Considered?

My SAT score is not competitive at many of the schools I am applying to (1940), but my subject test scores are solid (800 in WH for example).
My ACT is comparably better so I have already submitted that to all of the schools I am applying to but I am worried that in order to send my subject test scores I will also have to send my atrocious SAT I scores as well.
Should I submit any Collegeboard tests? Should I send them both? Should I bother self-reporting on CommonApp?

Any answers would be much appreciated. Specifically two schools I am concerned about are Brown and Rice, if anyone knows any specifics about either of those. Thanks.

You know the schools have web sites with info for this, right?

http://www.brown.edu/admission/undergraduate/apply/first-year-applicants

Rice is not quite so clear but states this:

https://futureowls.rice.edu/futureowls/Standardized_Tests.asp

I think @drusba sent a message to Rice asking for further info.

Thanks for the speedy response. My issue though is that it won’t let me unselect all of my SAT 1 scores from the score choice report. I looked at the website before but I don’t see where it says that if I send both ACT and SAT they will only look at the better one.