Building on what others have said --
Some TVs have a VNC client in their app store, or a network file browser. If you share the Recorded TV folder and your TV can see it, that'll mean you can try to browse directly from the TV. That said, if the TV can't directly play .WTV files doesn't work, try changing the extension from .WTV to something else. If that still doesn't work... You will probably need something to re-encode the .WTV files to something your smart TV can recognize. This can be accomplished a number of ways:
Do the transcode in advance --
MCE Buddy will automatically do the conversion for you. It can also strip commercials if setup correctly. Basically it's a MCE-centric front-end for a lot of other software it uses in the background (FFMPEG, Comskip, etc).I used to use this before I moved to a more integrated media management suite.
Other folks have used similar tools to MCE Buddy like VideoReDo. The purpose is the same -- Convert the .WTV file into something other media players like the one on your TV uses.
Do the transcode in realtime --
I've moved to apps that do the re-encoding from .WTV to something else in real-time as I watch on whatever device I'm choosing to watch it on (phone, TV, tablet, etc). I've got a decent computer, *for 2010*, as my MCE server. It's something like an i5-2500k with 8GB of RAM and a GTX 660. While it's not a raspberry pi (which could probably handle this too, actually), it's not some $10,000 server.
For Non-Copy Once (i.e. DRM Protected) Recorded TV, I moved over to using
Emby. The server runs on my MCE machine and it will do a real-time transcode conversion into something the Emby client running on my streaming devices can understand. I can also watch Live TV through Emby using something like
ServerWMC. The benefit of this is that it provides an easier to use UI experience than a file browser. If you don't have DRM issues, it may mitigate your need to use MCE as a front end at all as you can get full guide and recording/playback capability through the single client. (Note WMC is still needed if you want to do Live TV using ServerWMC)
I do not use Plex or Jellyfin, but my guess is they would work in a similar way to Emby -- if you can "play" the WTV file on the server, it'll transcode it to whatever the client app on your TV can use.
If you do not have any protected / copy-once DRM issues, you may also just be able to get away with some
Silicon Dust solution instead of WMC at all. Again it depends on if the Smart TV has the Silicon Dust app available in it's app store.
Finally, if you maintain a cable subscription, and the app is available, you could use
Channels DVR. That records TV Everywhere streams you subscribe to through your cable company. Note that it may not have full coverage of all the channels you get in your cable package. Some channels like PBS aren't available over TVE.
Note most of these solutions can have a cost associated with them. It's possible to do it for free, but you're generally trading time for ease of use.