Installing basement bath fan

I recently was forced to replace a basement bath fan. My basement is fully finished with drywall ceilings and walls. To my surprise I discovered that the original fan was never vented outside, simply just dumping inbetween the joists.
I would like to vent this outside, but my only logical options are to follow the joists with the vent pipe and go through the sill plate on top of the concrete basement wall and a 2 x 10 joist for my deck, or go a shorter distance through several joists a 2 x 10 and through the sill plate. I am not sure how this can be done easily without destroying the integrity of the exterior walls, as standard vent piping is 3 or 4 inches in diameter.
Anyone have any unique suggestions that would still provide good venting, such as using PVC/other piping with a smaller diameter. Or some type of reinforcement for the sill plate since there are already 2x10s for the deck? Maybe simply adding some screws in the area to fasten the sill to the deck joist more securely?
Thanks, Tom R.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.