OK. Many years of racetrack ponying, many ponies trained from greenies. Many racehorse first timers with the pony.
Get a leather shank. Rope is too bulky. Leather is easier to hold. English or western saddle doesn’t matter, use whatever you are comfortable in.
Unfortunately… the best rule of thumb to follow is… only one of the three of you involved should be green or first timers. That is… if the rider is green, both the pony AND the horse being ponies should be experienced. If the pony is green, the horse being ponied and the rider should be experienced. If the horse being ponied is green, both the pony and the rider should be experienced. Do you understand that? Multiple green partners is not a good idea.
Have the groom bring the horse up to the pony, let him look at the situation. His nose should be at the pony’s shoulder. Do NOT let the horse get further ahead than this, keep your leg in front of his chest. Do not let out too much rope, maybe a foot or so, if everyone is relaxed. If the horse gets too far ahead of you, he can kick your pony.
Start with the groom leading the horse alongside you and your pony, as all four of you walk along. When the horse is OK with this, the groom on the ground can try handing you the shank, and stepping out of the picture. Do this in an enclosed space, riding ring if possible, in case it doesn’t go well. Some horses are spooked by the sight of a rider up above their eye level, and will run backwards in fear. In that case, a GOOD pony willl be able to turn and follow the horse, so that you don’t lose him. A green pony probably can’t do this. A green rider won’t be a help either if this is a problem. May not be a problem.
When ponying, hold the leather shank with a few inches of slack from the halter. Room enough for some “play”, but not too long, nor too short. Hold the shank with your right hand, your reins with your left. Your pony neckreins, right? Along with the reins in your left hand, you ALSO hold the tail end of the leaather lead shank, a couple of coils. That way, if the horse runs backwards or balks, your rein hand is automatically activated, and your lead pony sticks with the horse you are leading. A good pony will follow any negative movement the horse makes, so that you don’t lose him. A green pony probably won’t. A green rider probably won’t either.
Have the handler who passed the horse to you remain walking with you at first, if you can. Your pony should be welcoming, not grumpy about this. The young horse will be perplexed, and may be frightened by what you are trying to do, not understanding the change in where the instructions are coming from. If your pony is calm and quiet and easy to get along with, more likely for success.
That’s kinda the basics for ya. Good luck.