As a language model, I can provide some general guidance on analyzing data related to cross-cultural adaptation, but please note that this is not a substitute for consulting with a qualified researcher or statistician.

In general, when testing the construct validity of an instrument without a domain, you can use exploratory and confirmatory factor analysis (EFA and CFA) to determine the underlying dimensions or constructs that the items are measuring. EFA is useful for identifying the number and nature of the factors in a dataset, while CFA is useful for testing a pre-specified factor structure.

You can also use item-total correlation analysis as a preliminary step to assess the construct validity of the instrument. Item-total correlation analysis involves calculating the correlation between each item and the total score of the instrument. Items with low correlation coefficients may suggest that they do not fit well with the overall construct being measured.

However, it's important to note that there is no single "correct" method for testing the construct validity of an instrument. The appropriate method will depend on the specific characteristics of the instrument and the research question being addressed.

Given that your instrument has ten items with no domain, it may be challenging to identify the underlying constructs without conducting a more in-depth analysis. One approach could be to conduct an EFA to explore the factor structure of the instrument and identify any underlying dimensions. Once the underlying dimensions have been identified, you can then conduct a CFA to confirm the factor structure.

Overall, it's important to carefully consider the research question and the characteristics of the instrument when selecting an appropriate method for testing construct validity. Consulting with a qualified researcher or statistician can also be helpful in ensuring that the appropriate methods are being used.