@kingoffrogs Sorry, might have misread - I thought it sounded like you were having trouble finding a harness that was fitting correctly, and then I saw mention of not being able to use a no-pull harness. You
definitely don't want to go that route as an option, just for your general information.
You would technically be hurting yourself on progress, but how much is fully dependent on the dog. It's going to be a bit confusing for pup, but might not be too bad. Perhaps a usable solution if the plan were to work extra hard on this and make enough progress during the alone walks that you'd soon be able to do this training when you have both dogs, in the not too distant future. Don't aim for loose leash perfection - aim for "good enough that the training can be done with other dog there". The sooner you get to the point of training consistently on every walk, the better.
For the loose leash training - less luring, more games that build engagement. You don't ever want to fall into the vicious cycle of having to dangle and lure with a treat to get the behavior you're after. That can be difficult to undo. The order should always be the desirable behavior is demonstrated and THEN the treat (or other reinforcement) appears. Teach these three things for best success: 1) dog learns super fun games happen when dog is near you and leash is loose, 2) actively train the behavior you want from your dog when they feel leash tension and 3) provide an alternative way for your pup to ask for side explorations without having to pull to try to ask.
1) Channel your best possible impression of a preschool teacher on a playground. Be animated and interesting. Praise and talk to your dog. Develop a "keep going" cue that indicates they're on the right track (I say "yayyyy"). Click and treat for check-ins. When dog is near you, launch into frequent games. Rounds of 123 game, counting steps or other pattern games. Praise and sudden treat scatters. Saying your dog's name and tossing a treat in a random direction. Asking for hand targeting. Change your walking speed slower and faster at random and praise and treat for responsiveness to the pace change. In short - do more to be awesome and create motivation for your dog to stay tuned in to see what crazy things you might do next. I recommend Leslie McDevitt's Control Unleashed program.
2) You want leash tension to be a cue in itself. When the dog feels it, what do you want? Decide what that is, shape it, and be ready to reinforce it tons. Dogs understand "do this" way more readily than they understand "don't do that". Turn leash tension into a cue. Mine was taught to slow down and then glance at me for a treat. Mostly he now just slows down and doesn't need the treat, but that wasn't the first step.
3) Dogs are dogs. They are going to encounter nearby smells that they just so very badly want to go investigate. If you've taught them that you expect them to stay glued to your side at all times with no deviation, they aren't going to stop having some of their own doggie desires and goals. Instead, all that will happen is that they'll resort to trying to attain their goals in the only way that comes naturally - trying to throw themselves at it. You don't want their goals and your goals to be a mutually exclusive situation. Provide tools for another way to ask. When my dog encounters something out of reach that he wants us to go to, he'll veer towards it, come to a stop as soon as he feels leash tension, back up a step and then stand looking at his goal. If he does this without jumping the gun and surging forward prematurely, I will release him with an OK and we will go over together. He's relaxed and happy and loose leash because he knows he doesn't have to try to steal and snatch at investigations that he wants. He has a way to ask that he knows is reliable. Pulling never gets him there - backing up and waiting DOES get him there. So, he does the latter.
Hope this helps you!