I have a need to connect nondestructively to an unpopulated header pin on a PCB. PCB thickness is typically 1/16" thick (1.59mm) but could be in the 3/64" - 1/10" range (1.19mm - 2.54mm); header holes are in the 30-40mil diameter range (0.76mm - 1.02mm).

Is there any kind of an off-the-shelf test clip / test hook that can reliably hook onto the inside barrel of a plated-through PCB hole in this size range?

I have used two methods.

The first is to use a 0.025” square post header. The diagonal of the square post is a little over 0.035”. The holes should be 0.036” to 0.040” to provide a snug fit. With test leads or wires connected to the square post header, there is enough side pressure between the post and the plated through holes to make electrical contact. I have used this for connecting to microcontroller debug headers on PCBs.

The second method is to use a spring type test point, such as the Keystone part number 5001, inserted into the plated through hole. The spring pressure against the plated though hole provides electrical contact.

I agree with waltz. 

My favorite spring loaded contacts come from Mill-Max

I'm not sure this is quite what you're looking for but these guys:

http://www.tag-connect.com/

do a wide variety of headers and clips, mainly for small footprint JTAG/SWD connectors. The through hole ones remove the need for a JTAG header on production boards which saves a bit of cost and also board real estate.

last time i have used just some square post headers and tilted theme a little so that there was solid contact. (similar as waltx mentioned)

next time i will try to use something like this:

www.feinmetall.com/product-finder/contact-probes/c...

there are different manufactures for these spring-loaded contact probes.

they are not locking themselves to the connections but if you press theme down its an reliable connection - and you are not fixed to a specific hole size. it can vary a litte...