You can't do that with BTC -> ShapeShift XMR -> XMR.to unless one of those services were taking a 3.78 BTC fee (not recommended to use such as service). You would need to use your own wallet in between.

Also, I'm not sure what sort of mix factors and such being used by shapeshift, so the normal caveats about Monero being optionally anonymous (and not fully mature) apply. Again putting your own wallet in the middle and being careful with timing could give a better result.