Bandsaw, Drill press, benchtop sanding station, these cut anywhere from 50% to 90% of the time for each "do the thing..."
clamps, you never have enough or the right type! i bought a Japanese style pull saw fine teeth cuts nicely . a proper fretting saw would be my next purchase.
space to work in helps. i have a deficit in this regard.
You may enjoy this post too then mike . ;-)
At the most basic, you could get by with a multitool. Mine has a saw blade and a file that, along with the knife blade and awl, could carve out the most retro of CBGs. It would be slow, but it could be done.
I'd recommend a coping saw (for curvy shapes) and/or dovetail saw (for fretting), a drill, and a rasp. Those four will let you cut any board to length, cut notches, sound holes, holes for tuners, and neck shaping. And grab some clamps (even the inexpensive spring clamps at Harbor Freight) for clamping the fretboard onto the neck while the glue dries.
I figure you already have a screwdriver, so I didn't include that. ;)
I tend to use the following tools the most (in rough order of use)
Of course, this doesn't count the various 'extra' stuff like the shop vac (*the* most used tool), clamps, rulers, etc.
I don't yet have a band saw or electric hand planer, although both of those are on my list (if I can find room).
Here's a cheaper alternative to the dragon rasp... if you're building necks from scratch, I picked up a Japanese Shinto Rasp that I love. Shapes the back of a neck very quickly and it's fun! Can't get the rounded corners like the dragon, but it depends on your build too.
Glenn Watt's video "The Easiest Way To Make A Cigar Box Guitar: https://www.youtube.com/watch?v=pmzvfyOizV8 lists the very basic tools you need.
The hand tools I use the most are all fairly cheap...
* .03mm lead mechanical pencil (to make very fine marks).
* .05mm lead mechanical pencil.
* 3' aluminum or steel ruler.
* 18" steel ruler.
* 6" steel ruler with increments to 1/64 of an inch.
* a 3" x 4" steel L-Square, either the one by Zona: http://www.hobbylinc.com/htm/zon/zon37-434.htm or the Stew-Mac one if you have deep pockets and want USA made: http://www.stewmac.com/Luthier_Tools/Tools_by_Job/Tools_for_Measuri...
* Hobby/Craft Square: http://www.hobbylinc.com/midwest-hobby:craft-square-precision-measu... it states that it has a 40 degree angle but it is 45 degrees. This is a very handy little tool.
* At least 4 each of every type and size of clamp in the world (ha, you think this is an exaggeration).
* If you are going to do hand shaped necks, the Stew-Mac Dragon Rasps may seem to be expensive but are really a bargain compared to similar files in both quality and usefulness (I have tried many). I have the small coarse and the small fine. The small fine is all I really use or need. http://www.stewmac.com/Luthier_Tools/Types_of_Tools/Files/Dragon_Ha...
However, many luthiers swear by the Shinto Saw Rasp which are cheaper than the Dragon Rasps depending on where you look. Still others prefer to use a small spoke shave (I just couldn't get the hang of using one).
* If you are going to do pickups/electronics, this soldering station is an absolute bargain. It accepts Hakko brand compatible replacement tips which are easy to find: https://hobbyking.com/en_us/soldering-station-with-adjustable-heat-...
Mine is about 5 years old and has been absolutely reliable.
* To help keep things clean and tidy, be sure to have a wet/dry vac. Even a small one like this is great to have around the house and not expensive at all: https://www.shopvac.com/product/shop-vac-1-5-gallon-2-0-peak-hp-han...
As you mentioned hand tools only, a draw knife does fast work on rounding a neck. On a straight grained piece of hardwood it is very easy to control and can leave the neck with virtually no sanding needed. For more curvy grain a farriers rasp eats wood like no tomorrow although it needs alot of smoothing afterwards. I found both of these at antique shops, old and stout and will last a lifetime. Also a nice sturdy bench is great to have, I feel for the guys working at the kitchen table or folding table.