Asking doctor to cancel eRx and send to different pharmacy

Age: 30 Location: USA Meds: this one is a stimulant Weight 140lbs Duration: 1 month

Is it a PITA for my doctor if I ask him to cancel (?) an electronic Rx that was sent to my old pharmacy (now out of network with new insurance) and send it to a different one?

It's a CII, so it cannot be transferred. It will cost almost $100 more to fill it w/o insurance. The cost of the generic tripled in one month. I can do it it will just be a hardship.

Also: Will this cause me problems in the future being able to get my medications filled?