Cubana and Conviasa seem to fly between Caracas CCS and Havana HAV.
However, lots of (business) travellers choose to fly COPA via Panama PTY between Venezuela because COPA has CCS-HAV thrice daily, Maracaibo MAR - HAV daily and Valencia VLN - HAV 4 x week. COPA aslo flies out of Port-of-Spain POS and Aruba AUA (somewhat easy to reach from Venezuela).
There're no "Budget airlines" in Latinamerica. A recommendation would be to check the COPA Vacation holiday programmes including airfare and hotel. Use the flight to Cuba, use the hotel nights and return w/ changed return date (but must inform airline when booking, not when in Cuba).