Can I shorten my prayers on a trip for something haram?

It depends on the school, and most scholars say no. The Maliki, Shafi'i and Hanbali schools hold that travel concessions like shortening prayers are not for a journey whose purpose is sinful. The Hanafi school allows shortening on any journey. Either way, you still have to pray, and the safest choice is to pray in full and rethink the trip.

Why shortening is a gift

Shortening the four-unit prayers to two when traveling is a mercy from Allah:

وَإِذَا ضَرَبْتُمْ فِى ٱلْأَرْضِ فَلَيْسَ عَلَيْكُمْ جُنَاحٌ أَن تَقْصُرُوا۟ مِنَ ٱلصَّلَوٰةِ "And when you travel throughout the land, there is no blame upon you for shortening the prayer." Quran 4:101

The Prophet ﷺ called it "a charity Allah has given you, so accept His charity" (Sahih Muslim 686). See What is qasr prayer? for how it works.

The majority view: no concession for a sinful journey

The Maliki, Shafi'i and Hanbali schools say a person whose journey itself is for a haram purpose is not entitled to travel concessions. Examples they give include traveling to steal, to cut off family, or to commit a major sin. Their reasoning is that a concession (rukhsah) is a help from Allah, and it shouldn't be used to make disobedience easier. So someone flying abroad mainly to gamble or to meet someone for zina should pray the full four units.

The Hanafi view: travel is travel

The Hanafi school says the verse and hadith mention travel in general without conditions, so anyone who travels the required distance shortens, even if the purpose is sinful. The sin is a separate matter between the person and Allah. Some later scholars found this view stronger in its evidence.

A sin during a normal trip is different

All schools agree on one distinction: if the trip itself is permissible, such as visiting family, a holiday or business, and you slip into a sin along the way, you still count as a traveler and can shorten. The disagreement is only about a journey whose main purpose is haram.

What should you do?

Don't stop praying. Whatever the trip, the prayer is still owed. Skipping it adds a second, bigger problem.
Pray in full to be safe if the journey is for something clearly haram. That satisfies every school.
Reconsider the trip. The question itself shows your conscience is working; listen to it.
Turn back to Allah. If you've already gone, repent sincerely; He loves those who return. See Will Allah forgive me if I keep committing the same sin?

Key points

Maliki, Shafi'i, Hanbali: no shortening on a journey for a haram purpose.
Hanafi: any qualifying journey allows shortening.
A sin during a permissible trip doesn't cancel the concession.
Praying in full is the safe option, and prayer is never dropped.

Tip: If you're tempted by a trip you know isn't right, swap it for a trip that feeds your soul instead: a weekend with Muslim friends, a nature retreat or a visit to a historic mosque. Same excitement, no regret.