From what I can see, the Card Caster could still use Spell Combat and Spellstrike with a one-handed or light throwing weapon that can also be used as a melee weapon, such as a Handhand axe or dagger. This is still quite different tofrom any other spellcaster.
However, they cannot Spellstrike when using the weapon in melee, due to the modififedmodified version of Spellstrike. They also could not use Spell Combat with a Deckdeck, which seems to make the archetype of limited use.