If you decide to try shims, you can use any construction grade lumber as the shim. The shims will be in direct compression, and wood is very strong in compression, so problems with shims are rare.
In order to insert the shim, you would need to loosen or remove the nails that are holding down the sheathing under the floor, then hammer in the shims until the floor is level. Alternatively, you can pry the floor up to level using a pry bar, then insert the shims to hold the floor in place. When installing headers to replace load bearing walls, it is very common to install solid wood shims between the jack studs and the header in order to get a perfect fit. This is especially common in retrofit situations where there is not always enough room to install a perfectly fitting jack stud under the header, especially if it is a steel header, so it is perfectly acceptable practice to install the jack stud up to 3/8 inch short, then shim to fit. Same idea if you shim your floors, except the load is much lower.