I'm a novice (not an expert) but I'll share what I learned in my recent DIY tiling escapade, which was also in my bathroom.

I have caulked a lot all over the house, inside/outside, and I never worry about exactly how large a hole I cut on the tip off the caulk. I just make sure it's large enough to easily fill the gap, and go back and smooth it with a wet finger.

On my bathroom tile, the corners weren't exact either, some tiles were a tiny bit closer than others, so I had the same problem with different sized gaps in the corners. No fear, just caulk it with a color than matches your grout, it'll disappear and blend in.

I was really surprised how easily the caulk came off the tiles, after it was dry. So really; I found it was easier than I thought: just make sure the gaps get filled, wipe it smooth so it looks pretty in the corner, and the excess comes off easy, after you let it cure.

What I'm trying say is that it's easier than you think it'd be.

My bathroom has baseboard trim, so I didn't have to caulk that edge in a visible way, it's covered up by trim. But I'd guess the same rules apply.

There should be no problem with the smaller joints. If you use the siliconized latex caulking that comes from your grout manufacturer, you can tool the joint with your finger after laying the bead of caulking, and then wipe it with a wet sponge until it looks like a normal grout joint. For the wider joints, using a sponge will pretty much just empty the caulking out of the joint, so your bets bet would be to tape off both sides of the joint with blue tape, and then take something flat and square (like a putty knife), and use that to shape the joint. IMMEDIATELY after hitting it with the putty knife, pull the tape. If you wait, it'll tear the edges of the caulk joint, making it look ragged.

Thank you both. I'll be down caulking shortly!