Your sinew job looks just fine!
Thats the way its supposed tp look.. it will feel somewhat sticky when you put your hand on it as your hand has heat and moisture and it will want to make the sinew soft..( especially if you used hideglue/knox gelatin) for the glue thats the reason to cover it with snakeskin... to keep the moisture out!
You will need to cover it with something,, skin of finish to protect the back from moisture
Looks good though,,, good job!