Do it in small bursts and hold the open body with the sensor facing down so gravity can help. If it makes it worse do it again until it gets better. Blowing the dust around can cause static to build up on the sensor and actually attract dust. Technically you are cleaning a protective glass shield over the sensor raher than making direct contact with the sensor itself.
I swear by the
arctic butterfly which is a dry method of cleaning the sensor by attracting the dust to a self induced static charged brush. It won't remove oil particles, that would have to be done with a wet treatment, but I don't find oil contamination to be the big problem some would have you believe. It is suggested the oils that are used in the assembly factory to lubricate internal moving parts are a big cause of image contamination.
I'm sure that can happen, but not to any great extent. You may be unlucky and have the camera body thst got more than it's fair share of lubricant, but I'm sure I read somewhere that chemicals used latterly bond far better are less likely to fall away from where they should remain.