So. . .
Loading the colonists into the ship without cargo shuttles is not a problem, but unloading them is impossible without cargo shuttles. 
Cargo shuttles to move the cryo-pods is fine as a game mechanic, but maybe a warning should pop up if a player designs a ship with a cryogenic transport but not cargo shuttles similar to the warning if a jump drive is too small.
It's not that you can load without, but only unload with. It's more that you need either a Space Port or a Cargo Shuttle Station at the colony or Cargo Shuttle Bays on the ship. You (usually) start the game with at least a Space Station on your home world, so this allows you to load without Cargo Shuttle bays, but since you don't have either Space Station or Cargo Shuttle Station on the receiving colony, you do need them.
But it is a good suggestion to add some kind of warning in case you don't plan to have Space Stations or Cargo Shuttle Stations on all colonies.
A lot depends on what is your design like. This should be seen as when you build jump capable ships. Would you invest in waiting a tender or a constructor to connect your JP or you simply get all your ship with a jump engine and the extra time and resources that this implies?
Personally, when I plan to go to Mars or Luna, I start building the Shuttle Stations first on Earth then I drop them off to the colonies so that my early colony and freight ships are already able to handle the job (except for those with cargo shuttles tasked to drop the installation off). If you do that then even the first 2 or 3 sector expansion is pretty much done without the need of redesign your early fleet entirely leaving you way more resources and science points (or blank research) to be invested into the military for protection of civ and commercial fleet. All you need is a construction ship and one scout to check the JPs.
There is no right way you just need to find your balance.
My Patrol Admin for First Contact is as follow:
1 diplomatic ship jump capable
1 scout jump capable
My Survey Admin for first Survey missions
2 Geo Survey Vessels not jump capable
1 Gravitational Survey Vessel (with the tender capacity to get the 2 survey vessels)
3 Escort (1 Leader with sensors and tender 2 craft missile capable just for basic protection)
My Logistic Admin for first system colonization
1 Constructor 180 days (will work on both ends. One year more than enough to get the First Survey mission going)
1 Colony Ship not jump capable
4 Freighters 25K each not jump capable
1 Troop Transport Brigade Level 50K not jump capable
Pretty much all the above vessels except the Gravitational Survey and The Constructor are built at start. The escort is borrowed from the military and usually has the latest available techs.
