eslHQ - Right Handman

I think you'll find, Martin, that hyphens in the type of construction you talk about are optional - some people use them and others don't. In the Grammar of Gontemporary English, Quirk et al point out that there are 3 ways of dealing with compounds - two word, one word and hyphenated, and say :

There are no safe rules of thumb that will help in the choice between these three possibilities... some may even occur in three different compound forms, for example flowerpot, flower-pot, flower pot

They point to the fact that the hyphenated form is tending to disappear. They say particularly in American English, but the Guardian Style Guide doesn't like them either : Our style is to use one word wherever possible. Hyphens tend to clutter up text...

They go on to say : There is no need to use hyphens with most compound adjectives, but then suggest they are useful when the phrase is ambiguous : A missing hyphen in a review of Chekhov's Three Sisters led us to refer to "the servant abusing Natasha", rather than "the servant-abusing Natasha".

They do recommend the use of the hyphen with cardinal/ordinal number + singular noun compounds (as in several of your examples), but a quick look at a concordancer shows that this is not standard. These examples ..
...where guests are accommodated in four two storey buildings,
... who cherish the five storey factory as part of the national heritage.
co-exist alongside ...
In a two-story house,....
Narrow four-story buildings ran the length of the block...

Interestingly, as these examples show (see the spelling), it's the American texts which tend to use the hyphen, while British texts often drop it. Checking a concordancer for the "right hand" example though, the majority of writers of both varieties do still hyphenate it. However, there are plenty of examples which don't:

Johnson unwired the right hand door,...
Less respect for the legal conventions was displayed by Castro's right hand man, Che Guevara,...
...the left hand program is finite but is not weaker than any finite syntactic approximation to the right hand program.

So, looking at the grammars/style guides and the general evidence, it's clear that there are no rules but that it's a matter of personal preference. From what I've seen of the evidence, it tends to be dropped more in British English than in American, but individual preferences will certainly also come into play. I'm British and I use it fairly rarely. Martin is British and clearly prefers to include it.