Almost anything you can cut with a tinsnips and/or gasket hole punch (for bearing cap bolt holes, if required) will work. My own preference is to use brass shim stock for this sort of application. Brass shim stock cuts easily and if it contacts a shaft journal, will not score the journal. I am fortunate in that I have a great deal of brass shim stock which was scrap or leftover from various alignment or erecting jobs I was on over the years.
On some jobs, where shim stock was not too plentiful, and where heavier shims were needed, I cut them from any sheet steel available. I have also made shims by cutting up welding electrode cans and olive oil cans.
A material which might work for your application, if you need a heavier shim, is aluminum. If you cut the shims from aluminum, a bit heavier than needed, you can 'polish' them down to required thickness. This can be done by rubbing on the shims on a sheet of coarse emery cloth or sandpaper laid on any handy flat surface (such as the table of your drill press). Mike the shim as you rub it on the emery cloth or sandpaper and keep going until you get the required thickness.
I've also made shims from thin 'reinforced phenolic' (aka "Micarat" or "Bakelite") sheet material when I needed 1/16" and 1/8" shims.
Some people have shimmed babbitted bearing caps using shims cut from manila file folders or thin cardboard such as some boxes are made from. Computer printer paper mikes at 0,004", and can be used as a shim as well. I've taken some old machinery apart and found shims made from things like 'time cards' (the kind you inserted into the time clock to 'punch in' and 'punch out' of work), and slips of paper.
Another material that is plentiful is soft aluminum beverage cans. These cut with common scissors. In the book "Zen and the Art of Motorcycle Maintenance", the author (Robert Pirsig) is going to repair a friend's BMW motorcycle. The problem is the handlebars are loose in the mounting clamps and there is no takeup left. Pirsig wants to cut shims from a beer or pop can, citing how the thin aluminum is ideal for shim stock. Of course, the BMW owner, an academic sort, wants no part of having his motorcycle repaired using shims cut from a beer can. For the application on a camelback drill, shims cut from a beer or pop can would be fine if thinner shims were needed.
An old bro of mine has had a saying that I've heard for the past 35 plus years that I have known and worked with him: "The solution to most problems is within 15 feet of them". Hence, if you go to your recycling container and fish out a couple of aluminum cans or find an empty welding electrode can laying around, consider it as shim stock. It's worked for me many times over and plenty of machinery has been levelled on sole plates shimmed with whatever was at hand, and plenty of babbitted bearings have had their clearance set with shims cut from similar materials.
I have brass shim stock down to 0.001" thick, which is basically a thin foil. That was from turbine alignment jobs and similar. It's rare that I use the 0,001" stock. I think the last time I used some was setting the clearances on a plain bearing lathe headstock. A rule to remember with shimming: if you wind up with a stack of many shims to set a bearing's clearance (or to level a piece of machinery), you have essentially built a 'spring pack'. Once you have determined what is needed to set a bearing's clearance, it is a good idea to try to reduce the number of shims to one or two heavy ones and perhaps 3 or 4 thin ones. The thin shims let you fine-adjust the clearance. After a shaft journal 'beds into' a babbitted bearing, the clearance sometimes opens up a bit. Having a thin shim or two in the shim pack on a bearing cap lets you take up for this 'bedding in'. I usually leave shims of 0.010", 0.005" and 0.003" as the thin shims and try to get the balance of the shims made up as heavy as possible. Cutting shim stock with snips or scissors usually leaves a burred or 'crinkled' edge. I bring a piece of flat steel bar that has been polished with emery cloth and a piece of maybe 1/2" OR 3/4" drill rod with me when I am cutting and fitting shims. I place the shims I have cut with the snips or scissors on the flat steel surface, hold one end down with my fingers and press and draw the drill rod over the shim. This 'irons out' the crinkling. For heavier shims as may be cut from sheet metal (like 16 gauge), I take a ball peen hammer and lightly hammer along the cut edges with the shim laid on the steel flat bar. This works down any wrinkling or slight burring. It does not take much to create a 'soft' shim stack if there are burrs or wrinkling on any of the shims. Over time, this will cause a looseness in the bearing cap and open up the clearance.
The stuff you are talking about weighs tons ! He's got a stinky little drill press. Pop off the caps, stick a squirch of gage in there, squeeze down on the caps, measure the clearance, adjust. Easy.
