If you put a line of unplated drill holes between the ICSP header and the rest of the board, with just enough space between the drills for the traces, you could probably just break the header part off.
It would be cool to have a jig you could press down over the top of the ATtiny with pogo pins to make the programming connections so you don't need the ICSP header at all but I'm not sure whether that exists or could easily be made. I know I've seen one for the TQFP-32.
There is also a standardized miniature ISP header footprint called Tag-Connect that's pretty nice. You do need to buy the ~$34 cable though.