I would suggest phrasing it like this. What it means is:

"by means of a letter signed by the assignor and the assignee or by a properly authorised representative of the one who [del que] does not act personally"

So the antecedent of "del que" is the cedente and/or the cesionario.

"No intervenga", being subjunctive, carries the implication that there may or may not be one of them that does not act personally (i.e. sign the letter in person), and indeed that it could apply to none, one or both of them. If either or both of them do not sign personally, their representative(s) must sign for them.

You might express it as "the properly authorised representative of whichever of them does not act personally", but that would imply that one or other of them will not, which may not be the case. The same problem arises if you use "the one who". The requirement for a representative to sign arises if one or both do not sign; it may not arise at all. So I would say "signed by the assignor and the assignee or by their properly authorised representative if they do not act personally". "Their [...] representative" corresponds to "representante [...] del que", and "they" is being used here as a bound variable (I was involved in an English-English question on this recently): in other words, referring to an indeterminate number of persons. The representative of each X, however many Xs there may be.

--------------------------------------------------
Note added at 1 hr (2013-12-09 02:39:29 GMT)
--------------------------------------------------

If anyone is interested in the question of singular "they" as a bound variable, the Wikipedia article is pretty good:
http://en.wikipedia.org/wiki/Singular_they

--------------------------------------------------
Note added at 4 hrs (2013-12-09 05:45:00 GMT)
--------------------------------------------------

I think Pablo's suggestion is good, and I'd endorse it as an alternative, like this:

"the authorised representative of such party or parties as shall not act personally"