Skywatch specifically doesn’t put the cast in a time machine, but the Whoniverse being what it is and genre telly being what it is, a time travel episode here and there is bound to happen. After all, Star Trek has plenty of them, including more than a quarter of the films.
(You can do all The Staples Of SF TV with illicit alien tech, as well, but let’s stick with the most Whovian oddity. I’ve left it this late so I’m not tempted to reel off the whole lot.)
Most genre shows do a one-off time travel episode at some point, including the Who spinoffs. Torchwood had these going in both directions due to the Rift on their doorstep, and a sinister time-aware cultist in town as well. The Sarah Jane Adventures had the Shopkeeper and the Captain, possibly a reference to Mr. Benn, sending the gang on vital-according-to-them missions through history. See also Blink, a mystery working backwards, where unintended time travel by the Doctor puts some normal modern people’s lives in great danger.
Like a Doctor Who story about time travel (rather than framed by it) a time travel episode of a normally-in-one-era show will generally focus on the mystery, strangeness and danger of time travel, play up paradoxes and predestination. Even restricting ourselves to Earth’s history, or the history of the place the group starts, there are plenty of ways to get in trouble.
And with no friendly time-travelling PC in the group, if the group don’t solve the mystery they could end up trapped in another century...
Since this will probably be your only time travel episode, give or take (I’d keep it down to one a series at most), make it a doozy.
These are normally historicals or these days pseudohistoricals (with or without a celebrity) so pick an era that really interests you and/or your players, find suitable visual aids (like stills of any of the cast in suitable period dramas), play up connections like ancestry and links like a ruined building restored to its former glory, bring up changing attitudes more than Doctor Who itself usually does, see how well they deal with living in history.
Let them fight Nazis, run from dinosaurs, nearly Grandfather Paradox themselves, meet and fall in love with people who died centuries ago, accidentally lead to the foundation of Skywatch...
Visits to the future in not-normally-time-travelling series tend to focus on near-future nightmares with roots in the present, a la Marvel’s Days Of Future Past. And then get back to the present just in time to fix it.
Show how amazing (and frightening, and dangerous) time travel could really be if you aren’t bouncing around the centuries every episode.
Example: The Portrait Of A Lady
(Borrowed from the time travel chapter in Cthulhu By Gaslight, Star Trek: The Next Generation - Time’s Arrow, and a plot hook dropped in Silver Nemesis)
When a wealthy UFOlogist goes missing, the Skywatch team search his Georgian manor house, catalogue various pieces of alien paraphernalia, detect some with residual energy signatures...
And one of them finds a Nineteenth Century painting, hidden in a safe, next to a file of press cuttings about Skywatch and photos of her and the others.
And the rest of the team see a flash of light, and run in to find the painting on the floor and no other trace of their teammate... a painting which appears to show her.