Funerals are not “absolutely required.” You could be cremated and have the plot where you are buried blessed by a priest. That probably would be the “bare minimum.” That said, I urge you not to settle for the “bare minimum” out of fear of “burdening” your wife and family. Care for the dead is not a burden but is instead a corporal work of mercy of which you should not deny your family the privilege to perform.
Expenses certainly can be controlled by planning ahead, by pre-paying whatever you can, and by choosing the least-expensive options (e.g., no embalming, a plain casket, cremation before burial). If your family’s finances are tight, church expenses can be adjusted according to ability to pay. But prayers for the repose of your soul should not be “curtailed.” By all means, have a funeral Mass and arrange for additional memorial Masses to be said for the repose of your soul. In eternity, you’ll be glad you did.