Is “complete conjecture” an oxymoron?

Supposition can be a false friend. Because a conjecture is a guess, a proposition, it might at first be supposed as an incomplete account of the truth or of an argument. This supposition lies at the heart of the idea that a conjecture is incomplete and that complete conjecture is an oxymoron.

However, according to definition a conjecture may be complete in itself. To conjecture that “The Earth is flat” is a full and complete proposition whose truth remains to be determined by evidence and argument.

Conjecture = an opinion or judgment that is not based on proof; a guess

Cambridge Dictionary

For the avoidance of the doubt expressed elsewhere, I add that my answer at least implies clearly (or, as I had hoped, says clearly) that the two word phrase complete conjecture is not an oxymoron

Oxymoron works on the concept of contradiction and opposition. I believe that the phrase 'complete conjecture' is not an oxymoron because the meaning of 'conjecture' does not incorporate completeness or incompleteness and, therefore, the term 'complete' is not exerting any contradictory meaning to 'conjecture'.

• This is a complete nightmare / guess and

• He's a complete idiot

use 'complete' to emphasise, with synonyms 'total', 'utter'. From Cambridge Dictionary:

complete [adjective] (very great) B1 [before noun]

very great or to the largest degree possible:

• The man's a complete fool!

However, the more usual sense of complete is 'fully comprehensive / whole / entire / missing no parts'

complete adjective (WHOLE) containing all the parts or pieces; whole:

• a complete set of dishes
• the complete works of Dickens
• We wanted a complete record of what everyone said.

[again from CED]

The problem with using the expression 'a complete conjecture' is that it is indeterminate; which sense of 'complete' is intended?

The 'comprehensive' sense is used with conceptual nouns, for instance in Is Populism an Ideology? A Refutation and a New Perspective Paris Aslanidis 2015 [Political Studies Association] we find

... of ideology to prove that populism is not a complete ideology by any established measure. Most scholars of populism refrain from asserting ...

And 'complete theory' is a well-defined term.

Whether 'complete' in this sense is also applied to 'conjecture', say with the Goldbach Conjecture, is possibly a matter for mathematicians.

Although it could be argued that 'This is a complete conjecture' could usually be inferred to be synonymous with 'This is a complete shot in the dark' from context, it could also be argued (and I'd be with this) that this is an unfortunate mixing of registers. I'd avoid it. But there's no paradox involved with the 'nothing more than', 'This is a total guess / conjecture' reading (though as I say, I'd choose a lower-register synonym).

The question is "Is “complete conjecture” an oxymoron?"

The OP has given no context at all but a "conjecture" may, in one context or another, be described, without ambiguity, as "complete."

OED

Complete: 1.a. Having all its parts or members; comprising the full number or amount; embracing all the requisite items, details, topics, etc.; entire, full.

For oxymoron, the OED gives

1. Rhetoric. A figure of speech in which a pair of opposed or markedly contradictory terms are placed in conjunction for emphasis.

1850 C. Anthon in Cicero De Senectute 164 In giving sensim its strict literal meaning, we will perceive here both an alliteration and oxymoron, the idea being, in fact, this: ‘life grows old so gradually that we perceive it, and yet do not perceive it.’

2. More generally: a contradiction in terms.

1993 Guardian 28 Aug. 22/5 This opened up an oxymoron too dreadful to contemplate: affordable caviar.

The answer is therefore "No", as complete and conjecture do not stand in this relationship.