To hold trumpets and cornets you can make a wood mandrel or special holding device. If you go to a unfinished furniture store they will have spindle type chair or table legs. Many large lumber stores have the same thing. Take a horn with you and find one which fits snugly into the bell section of the horn. It should be smooth without any decorative spinning. You can place this in the vice (get a good vice, preferably a machinist vice) and use it to hold the instrument while you solder or work on the slides.
I also use a piece of 2x4 wood stud about 12" long with two 2B drum sticks glued into it at a right angle(see diagram above). This is where a picture is worth a thousand words. The distance between the drum sticks is equal to the distance between the center of the 1st and 3rd valves. This type of holder is great for use when "Ragging" the valve section of a trumpet or cornet. You must remove the valves to place the body on the holder. Unlike the wood mandrel, this holder will not allow the horn to rotate. I make these holders to accommodate the horn I am working on at the time. It only takes about three to cover all the different brands. Make them as you need them.
To make the mandrels in the illustration, you may need the services of a carpenter. These mandrels must be turned on a wood lathe and carefully inspected for flaws. When I made these mandrels for the shop, I used 4x4's for the center of the tuba and F-tuba mandrels. This size is readily available at any lumber store. You may notice the discrepancy in the size between 4"x4" and the stated size of 3 3/4" . Due to factors unknown to man, lumber yards sell 4x4's and claim they are only 3 3/4" because they had to trim away the rough surface.To these 4x4's I attach the necessary amount of wood on all four sides to accommodate the taper produced after turning. It is only necessary to use white glue if you use untreated wood.
Although thee mandrels are big and bulky, there is no better way to hold these low brass instruments while cleaning or repairing them. These mandrels, if carefully made, will do no damage to the horns. They can be mounted in a vise and set to a level appropriate for the technician.
I have found the above sizes to work on the widest range of makes and models. You may have to modify them if you are using them for E flat, D tubas.