You have options ! First, if the grout is really gross it will hurt your sales price, so commit to fixing this. Second, you can use elbow grease with a grout saw to score and/or remove the grout. I see this for spot removal, not an entire shower. It is ugly work.
Third, a multi-tool with a grout attachment will make the job MUCH easier. You can get a cheap version of this tool at Harbor Freight or on Craigslist. Use it, re-sell it, get most of your money back. Re-grout, re-seal the grout, enjoy the profits.
http://www.homedepot.com/p/RIDGID-JobMax-3-Amp-Multi-Tool-Starter-Kit-R28600/202672276