I was in a similar state with a bow/bow character who wanted to grab some S&B skill so we could tank when needed. Just equipped the S&B to get the skill line started and did some side-quests, using class skills for damage. Made sure the right bar was active when turning quests in, so the skills levelled. It was about ten minutes play to get enough levels to start using the new skills as intended.

"Equipping S&B" wasn't just a one-handed weapon and a shield, however, it was the heavy armour set that went with it. The character already had a decent level in that from wearing a single piece with the five medium (and one light) all the time. If your character is wearing light for a magicka build, then you'd want to don a new set of mostly medium while they build up the weapon skills. That set should provide stamina, either max or regen, as you'll likely be short with the current build. Mine needed health/resistance from the equipment in order to tank better.

If you have (or can get easily) the extra set of gear, then you can swap "personality" for each quest you take on, depending on whether you feel confident of doing it on the weaker skills. Most dungeons will give you some pauses where you can change your mind.

Better yet, run with a group that can carry you a bit while you catch up!

I leveled every weapon skill line on my main, just because. Have your main weapon and its skills on one bar, fill in class and guild skills on back bar until you can start spending skill points. When questing or grinding dolmens, before you turn in the quest or the final pinion is released, swap to new weapon. Just make sure you have training traits on the weapons.