Which is more likely to be used in terms of KISS?

I have two functions. The first one:

public String getWeekDay(int day) {
    switch (day) {
        case 1:
            return "Monday";
        case 2:
            return "Tuesday";
        case 3:
            return "Wednesday";
        case 4:
            return "Thursday";
        case 5:
            return "Friday";
        case 6:
            return "Saturday";
        case 7:
            return "Sunday";
        default:
            throw new InvalidOperationException("day must be in range 1 to 7");
    }
}

And the second one:

public String getWeekDay(int day) {
    if ((day < 1) || (day > 7)) throw new InvalidOperationException("day must be in range 1 to 7");
    String[] days = {"Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"};
    return days[day - 1];
}

In my opinion both are simple and do the same thing but which is better to be used when it comes to KISS principle?

None of the above, you would use an enum for that and these already exist within Java 8.

https://docs.oracle.com/javase/8/docs/api/java/time/DayOfWeek.html

You should consider using an Enum, I think it fits more to your solution

enum  WeekDays
{
    MONDAY(1), TUESDAY(2),  //fill the rest days....

    private int day; 

    public String getDay() { 
        return this.day; 
    } 
}

And then check if your day exists in enum otherwise throw the exception, something like the below code

  for (WeekDays days : WeekDays.values()) {
        if (days.getDay() == dayToBeChecked){
            // your logic here
        }
    }

The second is more apt. For the newest java the switch expression would be nice too as it is more compact.

However better use the java time API for an English Locale.

/**
 * Return the weekday.
 * @param day 1=Monday till 7=Sunday (ISO standard).
 */
public String getWeekDay(int day) {
    return DateTimeFormatter.ofPattern("EEEE", Locale.US).format(DayOfWeek.of(day))
}