“however, I can only see publications stating that the HSE will only investigate if amputation below first joint, not that it isn't reportable as a major / specified.”

This is from the HSE incident selection for investigation criteria, which makes it clear that first of all the incident has to reportable under RIDOOR.( otherwise how would they know about it?)
Annex 1 – Revised incident selection criteria 1 October 2010
Criteria for selection for investigation of RIDDOR notifications (except gas incidents reported under Reg 6(1) and 6(2))
Fatalities - All fatalities as a result of an incident arising out of or in connection with work activities. This specifically excludes suicides* and deaths from natural causes.
Injuries to all persons, including non-employees, irrespective of cause that meet the following conditions:
1. all amputations of digit(s) past the first joint

http://www.hse.gov.uk/fo...c_admin_81.htm#selection

I know I'm a bit of a wuss, but not many of us are going to be able to do all our normal job functions 7 days after loosing a lump of finger.

My first riddor was an amputation - I phoned the hse infoline (which used to be really useful :-) in its day); the definition I was given at the time was if there was bone removed from bone then it was an amputation - which seemed reasonable enough to me.
HTH
Stu

Would appear at odds to their own selection criteria
http://www.hse.gov.uk/enforce/incidselcrits.pdf
Which as already been said states investigation needed if amputation below 1st joint. Well if you don't have to notify unless full finger how will they even get report to investigate!