amateur observing - Pinhole Projector: Can I use a specific solar optical eye piece to focus the Transit of Mercury?

The whole point of a pin hole projector is that it doesn't need any optics just a pin hole.

If you are after magnification then that is related to the distance you project the solar image behind the pin hole, with a projection distance of 1000mm the solar disc will have a diameter of about 9mm. Increasing the distance will increase the size of the image but also reduce its brightness. Increasing the size of the pin hole will increase the brightness but reduce the sharpness of the image.

I suppose you could use a handheld magnifying glass to look at a small image but would not personally recommend it as unless you are extremely careful there is always a risk of fire or even blinding yourself or someone else when using a lens near an unfiltered solar observation. There is a famous story of an experienced astronomer setting his beard on fire because he left the cap off his telescopes finder.