Subtitles are (usually) text files. You can open most if not all of these files (e.g. SSA, TXT, SRT...) with Windows Notepad, hence Word as well.
I don't know about Trados, but WordFast will skip over all timecodes.
One thing you have to be extra careful is that most of these files also have settings in the text. This is the beginning of a SSA (SubStation Alpha) file:
[Script Info]
Title:
Original Script: BR
ScriptType: v4.00
[V4 Styles]
Format: Name, Fontname, Fontsize, PrimaryColour, SecondaryColour, TertiaryColour, BackColour, Bold, Italic, BorderStyle, Outline, Shadow, Alignment, MarginL, MarginR, MarginV, AlphaLevel, Encoding
Style: Default,Arial Rounded MT-1,36,65535,16777215,16777215,0,-1,0,1,2,2,2,50,50,40,0,0
[Events]
Format: Marked, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: Marked=0,0:00:00.08,0:00:03.84,Default,NTP,0000,0000,0000,!Effect,{\i1}Our company has ...
[the beginning of the actual first subtitle text is shown in bold above - each subtitle has all that "stuff" that precedes it here, and includes the in/out times]
Be careful not to touch any of these settings, at least during translation. Later, if you know what they mean, you may edit them to get some useful effects.