I own the book "The Second Texas Infantry: From Shiloh To Vicksburg" by Joe Chance, which I would encourage you to purchase if you are interested in learning more about this regiment. It is probably the single best source of information on the 2nd Texas Infantry.
In the back of the book is a roster of all the known members of the regiment, divided by company. Abbreviated notes indicate such things as killed, wounded, missing or captured ... if applicable ... for each member of the regiment.
John P. Evans and W.W. Evans were both members of Co. C, The Bayland Guards, from east Harris and west Chambers counties, raised by Dr. Ashbel Smith.
Abbreviated notes after John P. Evans' name indicates that he was wounded at Shiloh and wounded at Vicksburg. There are no abbreviated notes following W.W. Evans' name, so he must not have been wounded or captured, etc. Based on this information, it seems likely that both men survived the war.
Are you related to these men? If so please write me back via posted message or email. I've done a fair amount of research on this regiment on this regiment over the years and would like to exchange notes with you if possible.