Consider using UL-listed lever nuts such as Wago 221s. IMO they are much better for DIY homeowners than traditional wire nuts.
To address your main concern, that you have limited space in the small junction box integrated into the disposal: Lever nuts use less space because they avoid creating a large solid bulky mass of twisted wire. The wires can be cut shorter, and after attachment they can rotate within the nut so it's easy to pack the nutted wires flat into the box. They all remain flexible unlike a twisted bunch of wires.
Other advantages: They require no guess work regarding wire length or nut tightness, they do not damage wires nearly as much if removed and replaced for any reason, it is far easier to correct mistakes, they are easier and safer for dissimilar wires (almost certainly true in your case), and they do less damage to old brittle home wiring. They make it easy and (relatively) safe to perform testing on live circuits. It is harder to use the "wrong size" nut because each wire has its own lever and there are only two common sizes of nut.
They require a little practice to develop skill and avoid mistakes but not nearly as much as traditional nuts. They are far more expensive than traditional nuts but for the limited use by a homeowner they would be a bargain at 4 times the price.
Note: Please be sure your disposal is equipped to properly mount home wiring (NM, MC, whatever you have) in place of its power cord and that you do properly mount it! If not, you are FAR better off installing an outlet near by and using the original power cord.