After careful consideration here's my recommendation for regrouting and or apply colorant:
1. Preparation is critical:
a) select the proper day, perhaps a nice warm day on the deck,..
b) prepare a nice meal or make reservations
c) select the proper beverage of choice, perhaps wine, or mojito's
b) bring along paper and pencil
a) with the stage set, explain to your significant other what's involved in getter a really nice looking bath.
b) present the 3 quotes you've gotten from good professionals
c) offer to take her/him to see the professional's work.
a) explain how long it will the professional to do it
b) explain how long it will take you to do it (if you don't know ask those DIY's on this forum)
c) bring out the paper and pencil and ask them to help you prepare a list of all the OTHER things you could do for them with that time.
4. Follow through --- do ALL those other things, then site back and enjoy. Remember, there may be another DIY project that you'd rather NOT DIY.
1. look back at option A.
2. well at least with the quotes you will know how much you're "saving"
3. keep careful track of cost and the time/labor so next time you can show the you saved like $2/hr!
Seriously.... Go do option A.
I have successfully torn all the tiles out, replaced board, and retiled and grouted the other bath about 10 years ago without any trouble. it is doable. But if you have tile with very small grout lines, and you value your sanity, there are better things to do with your life