Wowza server is able to ingest live mpeg-ts format but is not able to read it directly from a file. You may be able to use something like ffmpeg to convert the ts files to mp4 which should then work. Because you would just be changing the container format, it should be fairly quick as there isn't a need to re-encode.
With regular streaming, Wowza server just reads the file from disk or the live stream coming in from the encoder and then repackages it in a format that the player requires. This way, you can support lots of different player types with a single file or input stream. The stream format (h264 / aac) and bitrate are not changed so there is no extra encoding.
You do have the option of using Wowza transcoder that does re-encode the streams. This is used to create multi bitrate renditions from a single live source or to convert an incompatible live format (mpeg2 to h264 for example).