Wineskin(http://wineskin.doh123.com/Information.html) is an application for mac that makes simple wrappers for Windows-applications using wine, basically converting a Windows-application into a MacOS-application. (At least it looks so to the user). A readymade wrapper contains both the original application, some code from wineskin, and probably most of wine libraries as well. (at least some of them). But the wrapping is done on a complete .exe file, so it is not statically linked to wine or wineskin.
Both wine and wineskin are licensed under LGPL.
So can I just make a wrapper for my application and redistribute the wrapper from my website as freeware (proprietary, not open-source)? Do I have to publish the source codes of wineskin or wine?
How are things if I wanted to sell such a wrapper (as shareware or simply a paid application)? Do the same rules apply, are you allowed to sell those wrappers at all?
As far as I know how wine works, it does not modify the programs itself, but provides a wrapper to make them more portable.
So the licensing of wine and wineskin is for their own software only, but not for software wrapped by wine.
For example, the windows tetris game I copied over to my linux box must not be put under LGPL only because I run it under wine. That by the way would render wine useless: Things it has been made for, like executing windows applications on a free (debian) or even more evil systems (e.g. osx) ;) are mostly proprietary software not comming even close to a licensing in the sense of the LGPL.
So the same for your application: Only because you use a feature of some other application it does not mean that everything that gets in touch with that other application must be under the same license.
Only if you modify wineskin or wine itself, you need to publish your changes if you distribute the changed binaries of wineskin or wine.
If it's a community thing, you can think about to open source your skin so that users of your application can provide improvements more easily. But as far as I can assume that is not automatically a link.
As others have commented: When in doubt you have got two things to do: Get in contact with the original author(s) and ask for permission (easy) and second get in contact with a lawyer who can explain you everything in detail (harder). However, if you get permission by the original author(s), you're always fine. On the other hand, a lawyer can tell you what you can do/what not regardless of what others say.
A little review on the licenses first:
After this short review I would say that both Wine and Wineskin are available under the GNU LGPL 2.1 license.
The GNU Library or Lesser Genreal Public License (LGPL) allows redistribution of binary form along with your (non LGPL'ed or non GPL'ed) application. But this means you need to fullfill some needs as well. See sections 2 and 6 more specifically. Look for requirements for a "work that uses the library." as yours would be.
However there is no obligation for you to provide source-code of your application as long as it is a work fully under your control and not a derivate of any of the LGPL'ed code.