Moving the water supply down will most likley need the tiles removing and quite allot of destructive wall work and pipe rework required.
I would suggest maybe trying to put the new sink slightly higher(drill some new holes above the existing ones, and grind the old ones flush to the walls, taking care not to grind the tiles. trying to remove the existing threaded studs might cause damage to the wall and tiles) if possible at all. If you have a pedastal one then you might get away with it.
Here are some solution to decrease destructive reinstallation
Use a Copper to Flexi pipe. This pipe easily welds on to the ends that you have there and will conenct to any tap easily.
You can use a 90degree copper adapter to point away from the base possibly giving you some extra needed.
You also can use copper male adapters to manipulate the pipes.
One thing I learn in all the years of home building and DIY is that destruction should always be the last possible choice, even if it's cheaper because most of the time using some clever combinations can save you days of brick work, plastering etc. etc. etc. ...