There is no way that you should have to be without teeth for a month. You can have an immediate denture. The teeth are taken out the same time the denture is inserted.Dentures can be made to look like natural teeth and if you had to have your lower teeth extracted then the placement of two implants and an overdenture would be of great advantage to you for comfort and maintaining the bone structure. It is important that you understand exactly what is going to take place and that you have the utmost confidence in the dentist that is treating you. If this is not thecase then seek another dentist.
get another opinion and ask about an immediate/temporary denture.
I would say as a general rule you should save as many teeth as you can. About 6 years ago, I had 6 teeth removed and I regret it. At the time, it was very easy to have the teeth pulled because it was a fast solution that gave me quick relief and it didn't cost very much. I remember when I did this that my dentist and my oral surgeon were not really encouraging me to keep or restore these teeth. Looking back on it, of course I wish I would have restored what I could have because of the bone loss issue and because neighboring teeth are free to move around more because there are no teeth next to them. Please make sure that these teeth you are having removed really cannot be restored. I realize it may be expensive to restore them, but in the long haul you may be happy that you did it.
As for the denture, yes it's a strange thing they do with that. They extract and then put the denture in and really it is not as bad as you might think. Sure, it takes a while to heal and it takes a while to adjust to having this new thing in your mouth, but it time, it's all good.