During interphase II, there is no S phase in which DNA replicates. However, in this stage, do the chromosomes remain wound? Or have they unwound into chromatin form, and recondense during prophase II?
In many cases the chromosomes do undergo some dispersion, they do not reach the extremely extended state of the interphase nucleus, this all happens in telophase -I. It would be correct to refer to the stage between two meiotic divisions as interkinesis which is generally short lived.
The prophase-II is initiated immediately after cytokinesis, usually before the chromosomes have fully elongated.
According to the diagram found on this site, chromosomes do unwind during Interphase II of meiosis.
Sparknotes, although it's not necessarily a reputable scientific source, seems to concur:
Once the nuclear envelope has re-formed after the first meiotic division, the cell enters a short interphase. This interphase is not as specific as mitotic interphase; during meiotic interphase, chromosomes may decondense as the cell waits to proceed with meiosis.
Finally, this website provides a clarification in stating that there is no true "interphase" between meiosis I and II (I guess true interphase would be marked by replication of DNA which, as you state, does not occur):
The period between meiosis I and meiosis II is sometimes called "interphase," this is confusing because it is not a true interphase such as that seen between rounds of mitosis because no synthesis occurs (all chromosomes have two chromatids throughout this stage).
Interestingly, the very own existence of an interphase II between meiosis I and meiosis II is highly questionable, and a search on Pubmed found an article by Vernet et al., according to which interphase-II exists only in male meiosis.