doran's shield vs doran's blade on Shyvana??

Depends on match up but I would comfortably say, shield is almost always better for her

Depends on the match-up, tbh.

Although since she doesn't use mana, why not cloth/longsword with health pots?

D-blade, shes a lane bully, if you arn't abusing that then shes probably gana have a rough time anyways.

Never take ever on . and 2 pots is more gold efficient against ap bully's and with 5 pots is better against ranged ad. The reason is that you will be able to stay in lane longer with the latter items and pots since only gives you 80 hp and 1.2 hp per second then you have one pot which brings the hp up to 230. gives you 150 health and 2 pots so 450 health. Now has that extra -8 damage from champion autos but on average in lane you will be attacked about 26 times before first back so has an approximate total health value of 438 while is at 450, that's 12 more health and you won't need to sell it later. and 5 pots is better since you get 750 health and about 10% reduced physical damage. or if you know you can out duel your opponent. Which one you pick up depends on preference since gives you more damage and health over time while has better all in capabilities. Bottom line has 18 more health and 184 more gold, has almost 447 more health and 184 more gold.

doran shield has been proven to be pretty inefficient compared to other options

Doran's Blade. If you think they are even for your matchup, at least recognize that blade will make you last hit more efficiently.