Excluding the letter "A" (case-insensitive) from a country's standard English short name is a surprisingly tight constraint. Here are the universally recognized sovereign states that meet this criterion:
Correction on common list errors:
Verified "No A" List (Short Names):
Also: Cyprus (C-Y-P-R-U-S), Greece, Chile, Togo, Benin, Niger, Morocco (M-O-R-O-C-C-O — no 'a'), Turkey, Sweden, Norway (N-O-R-W-A-Y — has 'a'), Finland, Poland (has 'a'), Italy, Spain (has 'a'), Japan (has 'a'), China (has 'a'), India (has 'a'), Israel, Jordan (has 'a'), Lebanon (has 'a'), Oman (has 'a'), Syria (has 'a').
Final Clean List (Short Names, No 'A'): Benin, Chile, Cyprus, Egypt, Fiji, Greece, Iceland, Iraq, Israel, Italy, Mexico, Morocco, Peru, Turkey, Yemen. (15 countries).