Three friends of mine and I did the volcanos several years ago. No, you don't need a guide for the mountains but:
1) You will need to rent a car from the airport to Amecameca and Tlachichuca. DON'T drive at night as there are many cars on the highways and roads without lights.
2) I forgot the name of the family that keeps your car safe in Tlachichuca.
3) The native indians have a shuttle service from the town to the climbing hut. The fee is nominal. You WANT a ride to the hut as it is a long hike otherwise.
4) Be prepared for changes in the weather. A whiteout developed when we got to the rim. INTERESTINGLY, out of no where, two little dogs appeared out of the mist and led us to the top. Guardian angels???
We stashed our gear in the rocks away from the hut as thefts have occurred there.
Until you get to the snow, the climb will be grueling because the soil is all volcanic sand.
We did see a solo climber from France slip and slide down 1000 ft. We saw him get up and assumed he was OK.
If you have never been out of the U.S. be prepared for a culture shock, this part of Mexico is not Acapulco or one of the other tourist meccas - it is rural, with lots of poverty, homes without electricity or running water. For many people shoes are a luxury and the their mode of transportation is the burro, no BMWs there. The washing machine is the local river.
BTW, the best tortillas I've ever had were in Tlachichuca, freshly handmade; they were better than my grandmother's!
Our trip was successful without a guide because we did a lot of research months before about hotels, car rentals, the highways and probably because I speak fluent spanish ;-)