The month of Safar is not unlucky
There is a Hadith in Sahih Bukhari:
Translation: No disease comes on its own, taking something as ill omen is prohibited and there is no inauspiciousness in owl or in the month of Safar. (Sahih Bukhari, Hadith No. 5380)
Muhaddith-e-Deccan Hadhrat Abul Hasanaat Syed Abdullah Shah Sahab Naqshbandi Mujaddidi Qadri (May Allah shower His mercy on him) writes in the explanatory notes of this Hadith:
Translation: Imam Abu Dawood (May Allah shower His mercy on him) writes in Sunan Abu Dawood that Muhaddith Baqiya asked his teacher Muhammad bin Rashid about this Hadith and he said: In the days of ignorance, people used to consider the month of Safar unlucky, so the Holy Prophet (Sallallahu alaihi wa sallam) made it clear that Safar is not unlucky. Imam Qazi Iyaz (May Allah shower His mercy on him) says: With this Hadith, this superstition about the month of Safar is negated, that difficulties descend more in Safar. (Zujajatul Masabeeh, Vol. 3, Pg. No. 447)
With these lines, it becomes clear that considering the month of Safar is unislamic. Not marrying in this month or considering having celebrations as unreasonable is all wrong and is a remnant of the days of ignorance. They have no place in Islam.
Even if we look at the month of Safar historically, there is a Hadith that the Holy Prophet (Sallallahu alaihi wa sallam) performed the marriage of the Lady of Jannah, Hadhrat Fatima Zahra (May Allah be well pleased with her) with Hadhrat ‘Ali (May Allah be well pleased with him) in this month, although the famous narration is about the month of Shawwal. This narration is in Subul Ul Huda War Rashad, Vol. 12, Pg. No. 469:
Translation: Hadhrat Ja’afar bin Muhammad (May Allah be well pleased with him) says: Hadhrat ‘Ali (May Allah be well pleased with him) married Hadhrat Fatima Zahra (May Allah be well pleased with her) in 2 Hijri in the month of Safar and she came to live with him 22 months after the Emigration in the beginning days of Dhul Qa’ada. (Subul Ul Huda War Rashad, Vol. 12, Pg. No. 469)
Some people consider starting a journey in the month of Safar as unlucky, although the Holy Prophet (Sallallahu alaihi wa sallam) started for Madina from Makkah in the last days of Safar, as given in Sharh Zurqani ‘Alal Mawahib, Vol. 2, Pg. No. 102.