How to handle missing data when determining differences between groups using chi-squared or Fisher's exact test

I have 168 rows of patient data: 104 controls and 64 cases. I want to know if albumin status (low or high) is related to case/control status. I made a table using R:

> table(Albumin, Status, useNA = "ifany")
Albumin    Control  Case
Low    51       16
High   39       32
<NA>   14       16


As you can see, I have missing data. I did a chi-squared test on the entire table:

> chisq.test(table(Albumin, Status, useNA = "ifany"))$p.value [1] 0.006222513  Question: Should I perform the test on the 3x2 table above that includes the missing data? Or should I perform it on a 2x2 table that excludes the missing data, as shown below? > chisq.test(table(Albumin, Status))$p.value
[1] 0.01496166


Problem: In this example, both approaches yield significant p-values. However, I have other variables for which the difference is insignificant when missing values are excluded, but significant when they are included. I have some variables with only one missing value, as well.

Question: How should I apply the chi-squared test in those situations? Is my choice of test correct, or should I be using Fisher's exact test or some other test? And are there any diagnostics that I need to do before even applying these tests?