FAME are not extracted by a catalyst. It just increases the reaction speed. FAME are obtained by transesterificacion of oils and fats, but they are not contained in the feedstock as esters.
Concerning the possibility of other catalyst, for alkaline homogeneous catalysis there are no better option than both you mentioned.
You may use an acid catalysis by applying acid homogeneous catalysis but I don't recommend that. Alkaline catalysis is quite better.
On the other hand, you may think in use heterogeneous catalyzers or even enzimes. Examples of effective applications are a lot.
The biodiseal is produced commercialy by catalytic transesterification of oils. These processes are basically very similar but with plenty different details. Hundred reviews and tons of paper are published. What should you do is to read the literature. While you should not use your biodiesel as a fuel for any diesel engines. .
A lot of catalyst are used in the extracted oil to catalytically transform it to FAME which is reffered to as biodiesel.This process is called as transestrification reaction.
You can use homeogeneous catalyst and heterogeneous catalyst.
Now a days using renewable heterogeneous catalyst are being used for performing the transesterification of oils to fatty acid methyl esters.
You can check my published articles on using calcium oxide obtained from waste eggshells used as a heterogenous renewable catalyst.
To suggest you can still check with source containg- CaO,MgO, ZnO modified catalyst.
Apart from NaOH and KOH, you can also employ a hybrid catalyst some literature shows that alkaline earth metal oxides like MgO, CaO, SrO, BaO can be used as a catalyst for the transesterification process
Generally, you can use blending with diesel and use as automobile fuels
Biodiesel could be produced via transesterification where a catalyst is involved due to mass transfer resisitance of the reaction. Other than NaOH, KOH you can use NaOCH3 or KOCH3 these two catalyst are more active than NaOH and KOH also are homogeneous catalyst. If you looking for a heterogeneous catalyst I recommend you BaO, SrO over others since these two catalyst are highly activity as KOCH3 and NaOCH3. Between these methoxide, I recommend you to use KOCH3 over NaOCH3 cause NaOCH3 leads sasaponification which makes soaps and distrub layer separation. If you need any relatable publication reregarding catalysts on transesterification please vist below link.