I think whats important is that they keep the way the lense if focused correct....the way they are ground and placed in the frame (if I remember right) has a certain focus distance or something im really not sure of the right way to describe this , but if its cut down and its not kept in the right proportion, center, and what not it will really throw off your focus and what not and cause all kinds of focus havic with your eyes. but :) since you have an in with the optician dude if they are familiar with the grinding and fitting of lenses he should be able to do that for you. Many of the optical places though send their glasses out for that to be done though.
My answer is NO,if you want to have perfect eyeglasses!The most usual effect of re-cutting glasses is to change the PD(pupil distance) and that will be a problem!Of course there is a chance the technician to destroy the lenses,if the new cutting is not successful at shape!If you want so desperately to change your frame I propose to buy the same with different colour or much smaller plastic ones(you can change the shape of the plastic with heat) to achieve the best.
Theoretically, if your new frame is smaller than the old one or exactly the same as the old one, you can regrind the old lenses to fit the new frames. Moreover, the shape of the frame should exactly the same or approximately the same. That is to say, you can not regrind a round lenses to fit a rectangle frame. Moreover, you also need to considerate the possibility that your lenses will be destroyed during the processing of regrinding. So, the best option is to buy a new pair of eyeglasses.
Depends on the shape and if the prescription is still right, i.e. it hasn't changed so that you need a stronger one to be able to see, they can possibly be reground to fit new frames. Obviously it's more likely to be possible if the old lenses are bigger than the frames you want to use.