Tattooist's personalities vary just like the regular population, so how they might react is more known to you than us, assuming you've already had a personal consultation.
More than 9 times out of 10 you're drawing isn't even started 3 weeks in advance.
Go and visit the artist, if it's feasible - and express the above. E-mail should be a workable option, too.
I've got an appointment in 3 weeks time but I've been having thoughts about changing the design. I thought I was dead set on what I wanted but then I wasn't sure about size and placement as I thought I wanted it smaller but my initial design wouldn't look great smaller. I've just thought of another design that would work smaller. Also as this is a tattoo for my son I feel this new design is more indicative of our bond so I want to feel completely happy on a personal level that I choose a tattoo that reflects our bond best. Im just frustrated with myself that id never thought of this idea before as if I had, I would've gone with this rather than changing my mind. As a tattoo artist, would you feel annoyed about having to change design 3 weeks in advance? How likely is it that you would have drawn the original idea up this far in advance? Im happy to pay a bit more if she has already drawn it and therefore needs more time to redraw new design, ive already paid £100 deposit so not sure how much more generally I'd need to pay. I know every artist is different though.