I have just tested on a stock standard installation of XAMPP 1.7.3 and all browsers you listed including others like Iron Portable, SeaMonkey and Pale Moon require me to accept the certificate offered with no problems when I do.
The conclusion to that is perhaps you have an issue with your 1.7.3 installation as OpenSSL is working and serving the https pages by default - I don't know anyway of telling what maybe wrong with your installation except to check that you have the folders \xampp\apache\conf\ssl* and these lines are not commented out in your httpd.conf file
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# Secure (SSL/TLS) connections
Include "conf/extra/httpd-ssl.conf"
and you do indeed have the conf file in the extra folder.
In the httpd-ssl.conf file make sure that these lines look like this
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#
# When we also provide SSL we have to listen to the
# standard HTTP port (see above) and to the HTTPS port
#
# Note: Configurations that use IPv6 but not IPv4-mapped addresses need two
# Listen directives: "Listen [::]:443" and "Listen 0.0.0.0:443"
#
#Listen 0.0.0.0:443
#Listen [::]:443
Listen 443
If you just have 0.0.0.0:443 uncommented then this may be the issue you are having, so change it to the above, save the file and restart Apache.
You can also check you have these 2 files in the \xampp\apache\bin folder:
openssl.exe
openssl - looks like a shortcut but if you drag it into an open text editor it will reveal the openssl.ini file.
Run \xampp\xampp-portcheck.exe and make sure Apache (HTTPS) has httpd.exe on port 443
Good luck.