"Usted" here is the notary. This occurs in draft contracts (minutas), addressed to the notary, telling him/her what is to go in the contract, which the notary will then draw up for signing. So the future tense, "you will say" is an implicit imperative: this is what you are to say. But of course this is not normal practice in UK contracts. If you take the line that everything ought to be translated, then I think the appropriate translation would be "You are to state that", but I don't think anything is really lost if you omit it. As you say, it is sometimes included and sometimes not, and whether of not it is there is really random.

Here are a couple of Bolivian examples to show how it works. They begin by addressing the notary and asking him/her to draft the contract in his/her register of documents:

"MODELO DE CONTRATO
CONTRATO DE INTERCONEXIÓN
DE REDES PUBLICAS DE TELECOMUNICACIONES
Señor Notario de Fe Pública:
En el registro de Escrituras Públicas a su cargo sírvase insertar el presente CONTRATO DE ACUERDO DE INTERCONEXIÓN DE REDES PÚBLICAS DE TELECOMUNICACIONES, en adelante denominado el "CONTRATO" [...]
PRIMERA: PARTES CONTRATANTES.-
Dirá usted que celebran el presente CONTRATO:
1.1 LA EMPRESA DE TELECOMUNICACIONES XXXXXXXXXX [...]"
https://att.gob.bo/sites/default/files/archivospdf/Modelo de...

This one has no more "Dirá usted"; it's understood in what follows.

Here's another, which has it in clause 2 but not for the parties:

"SEÑOR NOTARIO DE FE PUBLICA .-
En los registros de Escrituras Públicas que corren a su cargo, sírvase insertar una de Contrato de Arrendamiento, bajo lo siguiente.-
[...]
S E G U N D A.- (ANTECEDENTES, INMUEBLE).- Dirá usted señor Notario que la PROPIETARIA, declara ser única y legítima dueña de un inmueble [...]"
http://www.galeon.com/cochalaw/contratox1.htm

I think it'll sound odd if you translate it.