"Tight" as in small space or the nuts on the faucet are tight?

You shouldn't have to take the sink down. When you buy a new faucet you will get new handles and a spout so just replace the whole thing to keep it matching.

Are you able to remove the water supply lines?

While changing the trim on individually controlled lav faucets cam appear simple, the splines may not match or the height of the escutcheons may be different.

There are a couple of "under the spout" connections and this is one of those;http://www.deltafaucet.com/customersupport/documentation/35713lf.html?document=pd&fromDetailArea=bath&documentIndex=#flashWrapper

So you can see what you are facing.

A basin wrench is the most common tool or an open end which attaches to a 3/8" extension.

In most cases the spout and threaded shaft are separate from the "T" that the water supplies connect too.

I'm in agreement with previously posted so I will only add. Unlike electrical devices,plumbing parts can be a real pain to replace one part of an assembly,so think about replacing the facuet. At any rate removing the sink is usualy quicker and generally better results. The bowl and pedistal are normaly seperate pieces. The bowl SHOULD be hung on a wall mounted bracket. If so,the bowl lifts straight up without removing screws holding bracket to wall. I wouldn't let the grout scare me off. A few hammer wacks to a stiff putty knife should crack the grout with no harm to tile or sink. A sharp putty knife or heavy duty razor scraper will claen grout off sink and tile once sink is off the wall. With everything clean,you can use a good quility caulk if you arn't comfortable grouting.

Thanks for the input. I will be replacing the faucet with the exact one I have. the basin wasn't attached mechanically to the wall. It was siliconed and then grouted.

My biggest fear is basically screwing up my tile and/or the porcelain.

The tight fit isn't the nuts but actually getting my hand and tools to access the nuts.

But I think removing the basin is the best bet.

I guess if I painter's tape the tile and the sink and gently tap at the grout I should be okay.

Before you remove the sink, mark the bolt holes.
As described, crack the grout.
Silicone should retain some flexibility, so cut what you can and then insert some shims, cut some more and push the shims.
The sink skirt will be wide enough that you can drill and insert a 1/4" molly, with a fender washer when resetting the sink.

Remove all of the silicone and use POLYSEAMSEAL, it tools with your dampened finger remain flexible for 20yrs. and if your good, can be mixed to match most grout colors.