Quicktime Player 10 can do no-encode trimming of several codecs, including H264: https://support.apple.com/en-us/HT201066
I thought the TRV350 was a tape-based consumer camcorder that pre-dated DV. In those you would typically capture the tape in real time using Firewire to a computer.
After capture from tape if the on-disk codec doesn’t allow trimming by Quicktime Player 10, you’ll have to use FCPX. Import, edit then export to ProRes 422.
However given the limited resolution of that camcorder you probably could not see any difference if you exported to H264 via File>Export>Master File>Setting>Computer. FCPX uses a fairly high bitrate for that encoding.
If the on-disk material is interlaced (which was common in that era), *that* is a bigger quality issue than theoretical generation loss from re-encoding. It is easy to accidentally pick a project/export option which doesn’t handle this well.
If it’s interlaced, you might want to “hard deinterlace” that in FCPX since most playback devices today expect progressive scan material. One way to do this is create a new project with “use custom settings”, use something like 720 x 480 and 29.97 (if appropriate), add the material to the timeline, select those clips, then in the Inspector “info” tab pick Settings at bottom to expose the deinterlace filter, check that, then export. The output will be hard deinterlaced.
VLC allows turning deinterlace processing on/off. You can compare the image quality of the original camera clip with and without VLC playback deinterlacing to the hard deinterlaced clip you export from FCPX and determine if it’s OK.