To be honest, I would much prefer a larger fleet of smaller ships to a smaller fleet of larger ships. Something like pocket carriers, corvettes, and cruisers compared to full blown destroyers and frigates. The reason being is that you have little invested in each ship. If one is eliminated, its not a significant blow to your operation assuming it wasn't the command vessel. Smaller ships with quicker recharge jump drives would enable the fleet to use harrassment tactics against a larger force. Now against the Shivans this sort of strategy might work better than you think. Shivan ships in general seem to have no concept of strategy whatsover. As a species they seem to apply one strategy; throw everything you've got at the enemy until he's dust, his planet is dust, and his fleet is a floating debris pile. Using smaller ships, the GTVA could stay mobile, and thus fight engagements only when the odds are in their favor. In addition, since the Shivans are relentless, using smaller, faster ships to draw out the Shivan big guns would be an effective way to eliminate chunks of the Shivan fleet. Shivans have little in the way of anti-fighter defense (The Ravana, Demon, and Sathanas anyway. Fly in circles around them all day with narry a scratch). Because of this, luring a destroyer or juggernaught into position, then either launching bomber attacks or deploying a stealthed meson bomb(not really sure if that's possible, but it would make for one hell of a nice surprise) would enable the GTVA to pick off larger targets with little risk to the main fleet.
Now some might argue that the Sathanas would just unleash all of its fighters to stop the incoming attack and thwart it. The best way to handle that is to have a small fighter escort guarding one of the smaller ships, causing the Sathanas to hopefully launch its fighters while its still out of beam cannon range. If it launches even a third of its fighter compliment, that is a significant boost to the strike force. If said bombers are accompanied by two or three cruisers or corvettes to provide fire support, the Sathans can be ambushed, crippled, and destroyed with probably minimal loss of life on the part of the attackers.
When fighting an enemy who has both superior numbers and firepower, you make him come to your yard.