Shoulder patch

Navy enlisted men had ranks and rating. The chevrons denote his rank. The X is his rating.

Judging by your statement that he was a member of the UDT, the could have been for one of these ratings:

• Specialist (Not Elsewhere Classified) 1943–1948
• Armed Service Radio Service and Special Navy Radio Units 1945–1948 (to ESX Radio Broadcasting Technician)
• Artist 1945–1961
• Bombing Trainer Instructor (V-10) 1945–1946?
• Cable Censor 1945–1947? (to ESK Telecommunications Censorship Technician)
• Cartographer 1943–1948 (to DM Draftsman)
• Discharge Interviewer 1945–1948 (to PN Personnelman)
• Engineering Draftsman 1943–1948 (to DM Draftsman)
• Intelligence Duties 1944–1948 (to ESX Naval Intelligence Specialists 1948–1961)
• Key Punch Operator and Supervisor 1944–1948 (to MA Machine Accountant)
• Operations - Plotting and Chartwork 1943–1948 (to ESX Chart Clerk 1948–1961 and AC Air Controlman)
• Pigeon Trainer 1943–1961
• Plastics Expert 1943–1961
• Strategic Services 1945–1948 (to ESX Special Projects OSS 1948–1961)
• Telephone Switchboard Operator and Supervisor 1943–1948 (to ESX Switchboard Operator 1948–1961)
• Topographic Draftsman 1943–1948 (to DM Draftsman)
• Visual Training Aids 1943–1948 (to ESX Model Maker 1948–1961)

There are other ratings that used an X, but these are the most likely.