Hello David,
I suggest that the likelihood of success of BS1 centre-drill to 're-drill' your wayward holes depends on how much out of true your existing 2mm holes are. The point diameter on a BS1 centre-drill is 1.2mm, provided that point doesn't touch the walls of your already drilled 'wandering holes' at any point when drilling through then with the work firmly held and the centre-drill securely oriented and progressed into the job with great delicacy and patience your scheme will work. So, the success of your proposed centre-drill method depends on the waywardness of the existing holes. You do need to be confident that the point will not 'snag' the hole-wall at any point as should the point of the centre-drill touch the wall of the already drilled hole at any point as it progresses then it is likely going to fail.
If you prefer a less risky method then I would suggest a suitably sized slot-drill (likely 3mm?) to re-orient your wandering holes. Once again rigidity, delicacy and patience will be the watch-words.
Best of luck(!) & regards,
Phil
Edited By Weary on 27/02/2019 18:30:09