The English sentence is ambiguous, "their" might refer to "they" or to another group of people. Likewise, the Swedish sentence "De visar deras skor" is ambiguous in the same way. The sentence "De visar sina skor", however, isn't. There "sina" refers to "de".
So, yeah, it should be correct.
Visa is the infinitive (att visa = to show) and imperative (visa! = show!) for of the verb. Visar is the present tense (jag visar [...] = I show [...]).
The first sentence means Show me your shoes! while the second one is grammatically incorrect. Two possible corrections are:
- Visar du mig dina skor? = Do you show me your shoes?
- Du visar mig dina skor. = You show me your shoes.