How can I get the shadow blue dye without buying it on the market?

I had a chance to get it in the anniversary pack I opened, but stupidly got another one that sells for only a few gold which I ended up not liking much. Now I wish I had gotten the shadow blue but it costs 39 gold on the marketplace.

The anniversary pack was you best guaranteed chance outside of buying it directly. You could wait for the Shadow Dye Kit to come around on sale again, but that would be a gamble with each one you open.

Best option: Do some farming or fractals; sell off what you've gathered until you get the 39g; enjoy your well earned dye. (This is assuming you're not going to get another anniversary pack any time soon).

The dye pack is by character, right? If so, do you have another character that's coming up on the same age?

Exclusive dye prices can be pretty volatile, but as supply doesn't increase unless the kit containing the particular dye becomes available in the gemshop, you're probably going to have to wait awhile for that price to come down significantly (it looks like it last dipped below 10g back in January-March of this year).

Alternatively, you could purchase a similar dye that costs less. I find that Midnight Ice dye looks almost exactly the same as shadow blue on a wide variety of pieces. This dye costs only a small fraction of what shadow blue sells for. If you don't already have it, I'd look into it.