The car does not have to be running. I would replace both as long as you are doing it (cheap insurance). One person bleeding without a bleeder tool (or second person) is not easy but it can be done. The trick is not to let air back into the lines when the brake pedal is released from the depressed position. On your new wheel cylinders attach a piece of clear tubing (20 inches or so) that fits snug onto the bleeder screw. Your new bleeders should move very easy but if you want to use a boxed end wrench you need to put it on the bleeder screw before you attach the tubing. Now you need two clear containers (like a plastic pop bottle with the sloped top cut off). Place these on the floor and put the clear tubing into the bottle. Tubing should go all the way to the bottom. Next partially fill the bottle with brake fluid so that the bottom of the tubing is below the level of the fluid. This will stop air from being sucked into the brake line if you make a mistake or the brake pedal holder slips off. Speaking of the holder, it can be a piece of wood, a long screw driver, a long wrench, or what ever will keep the pedal in the depressed position after you take your hand/foot off the pedal. You will need to wedge it between the pedal and the dash support. This holder will act as your second person while you slide to the back and tighten the bleeder screws. So it goes like this: Bleeders open and tubing below brake fluid level in containers. Gently push the brake pedal down. Once down, use your brake pedal holder to keep the pedal depressed. Go to the bleeders and tighten both up. Go back to the brake pedal and release your tool. Allow the pedal to come back up (you may have to lift it). Return to the rear bleeders and loosen both again. Gently depress the pedal to the floor again and wedge your tool in to hold it down. Once again you will have to go to the rear and tighten the bleeders back up. Repeat, repeat, and repeat as you are trying to fill the lines and the wheel cylinders. There is no pumping, that comes later. Remember to constantly check the fluid level in the master cylinder and add as needed. Some people will start with the longest rear line (passenger side) and leave the other one tight. When you see few or no air bubbles in your clear lines you can now start adding pressure unless you were doing one side at a time. In that case you now need to leave the long side bleeder tight and only open and close the short side. Regardless, once there are few or no bubbles in both lines you can tighten both bleeders. Now you can pump the brake pedal until it feels firm. Once again, wedge your pedal down. Then go back the the long brake line, and open that bleeder only. There should be a blast of fluid through the clear tubing. This release will also allow the pedal to drop and your wedge will probably fall off the pedal. No fear, as long as the tubing is under brake fluid you will not suck up any air. Tighten the bleeder back up and repeat, staying on the long brake line side. After several times on the long side (and few air bubbles being seen) you can switch to the short line side wheel cylinder and repeat the process. The brake pedal should get more firm as you proceed.
Once you think you have the air out of both wheel cylinders you can fire up the engine (this will add a lot more pressure) and repeat the process of bleeding again. Pumping the brake pedal until firm, insert the wedge, and then shut off the engine. Do your side to side bleeding until the fluid in the clear tube flows clear, without bubbles.
This whole process is a pain in the *** with all the getting in and out, opening and closing of the bleeders, and wedging of the pedal. It will work but without a person's leg to force the pedal to the floor when you open a bleeder, it will take longer, a lot longer!!!! Without the pedal stroke you are only removing a very small amount of air each cycle so it burns up some time. I have heard that some people "gravity bleed" but I have never tried this method so I have no idea if it works.
There may be an easier way to do one person bleeding without the proper tools (others may know of one) but this will work.
Best of luck to you.
