The fundamental problem you have in adding a character mid game is that the number of loyalty cards in circulation has to change. As to the options you proposed, having a character inactive but dealt loyalty cards is a bad idea because it throws off game balance. For example, if there is a five player game, there are two cylons in circulation (as opposed to the one cylon in four player), making it far more likely that a cylon will be present before sleeper phase, but with one fewer human to balance that out this would severely disadvantage the humans (who already have the weaker position in the base game). Instead, you actually do want to change the composition of the loyalty deck and deal in a new character when they get there, as long as it is before sleeper phase. In the situations below, you construct the initial loyalty deck based on the number of players you have at the time, and will modify the deck when a new player (or possible multiple) join. And, yes, I have actually done this in a game.
After Sleeper Phase (not recommended):
If it is after sleeper phase, all loyalty cards will have been dealt, making it very difficult to add a new player without incident. If you are playing with an odd number of players to start, you can have the new player join as the sympathizer, but even this is really bad from a balance perspective as the sympathizer condition will almost certainly fall in favor of the humans late in the game. Having the new player join as a cylon leader (see below) is the best option from a balance perspective, but probably sucks for the new player. You should probably just finish and start another game.
Adding a Fifth Player:
If you start with four players and want to add a fifth, then you are going from having one cylon and a sympathizer in circulation to two cylons and no sympathizer. Don't shuffle the sympathizer into the loyalty deck until sleeper phase (if you already shuffled it in, you will need someone who is not in the game to remove the sympathizer from the loyalty deck, as the cards still in the loyalty deck give away hidden information about the current game). Then, when the new player joins, put the sympathizer back in the box, shuffle one not-a-cylon card into the deck (two if the new player is Baltar or Boomer), shuffle a new cylon card into the deck, and deal the new player starting loyalty card(s). This will make the new player more likely to be a cylon (which means the new player is suspicious, and is rather accurate in terms of the show) but is about right in terms of game balance.
Adding a Fourth or Sixth Player:
Meanwhile, if you start with three or five players and want to add another, this isn't too bad. Shuffle one not-a-cylon card into the deck (two if the new player is Baltar or Boomer), deal the new player starting loyalty card(s), and take the sympathizer out of the box, to be shuffled in to the loyalty deck during sleeper phase.
Adding a Cylon Leader:
Another good option is to have the new player be a cylon leader (if playing with the Pegasus or Daybreak expansion), as this doesn't change the distribution of loyalty cards, other than needing to replace the sympathizer card (if relevant) with a not-a-cylon card. The new player will be at a slight disadvantage going in, having less time to execute on their scheme, but that's what they get for showing up late.
Notes for Expansions:
The Mutineer from Daybreak should behave the same as the sympathizer according to the instructions above, with one exception: if the new player starts as a cylon leader, do not change the composition of the loyalty deck at all (i.e. do not replace the mutineer with a not-a-cylon card).
If you are playing with the conflicted loyalties variant from Exodus, you're on your own on for making an adjusted loyalty deck work.