Answer : No, dijon mustard with even a little white wine would be impermissible.
Wine is both impermissible (haram) and filthy (najis), whether in small or large quantities, whether or not it intoxicates. This impermissibility is affirmed by scholarly consensus (ijma`), given the clear texts of the Qur’an and Sunna prohibiting wine, unconditionally. [Nawawi, al-Majmu` Sharh al-Muhadhdhab; Ibn al-Humam/Marghinani, Fath al-Qadir `ala al-Hidaya; Ibn Abidin/Haskafi, Radd al-Muhtar `ala al-Durr al-Mukhtar]
The Prophet (Allah bless him and give him peace) was asked about the used of wine for medicinal purposes, and he replied, “It is not medicine. Rather, it is an ill.” [Muslim, Abu Dawud, and others, from Tariq ibn Suwaid (Allah be pleased with him)] If wine is impermissible even for potentially-beneficial purposes, then it would–a fortiori–be impermissible for other uses.
That is why the jurists of mention, as stated by Imam Ala’ al-Din al-Haskafi (Allah have mercy upon him) in al-Durr al-Mukhtar, commenting on the words of Imam Tumurstashi’s Tanwir al-Absar,
“(Both a little and a lot of it is prohibited) by scholarly consensus (in itself) meaning, in its essence–because of Allah Most High’s words, ‘[O believers], truly wine and arrow-shuffling, [idols and divining-arrows are an abomination, of Satan’s work; so avoid them completely so you will prosper. Satan only desires to precipitate enmity and hatred between you in regard to wine and arrow-shuffling, and to bar you from the remembrance of God, and from prayer. Will you then desist? And obey God and obey the Messenger, and beware; but if you turn your backs, then know that it is only for Our Messenger to deliver the Message Manifest.]” (Qur’an, 5.90) [Haskafi, al-Durr al-Mukhtar]
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1252 – وَعَنْ وَائِلٍ اَلْحَضْرَمِيِّ; أَنَّ طَارِقَ بْنَ سُوَيْدٍ رَضِيَ اَللَّهُ عَنْهُمَا – سَأَلَ اَلنَّبِيَّ – صلى الله عليه وسلم – عَنْ اَلْخَمْرِ يَصْنَعُهَا لِلدَّوَاءِ? فَقَالَ:” إِنَّهَا لَيْسَتْ بِدَوَاءٍ, وَلَكِنَّهَا دَاءٌ” – أَخْرَجَهُ مُسْلِمٌ. وَأَبُو دَاوُدَ وَغَيْرُهُمَ ا (1) .
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