Welcome evertvaningen
To blacklist any module simply add the modules to the boot config file 
Append this boot code to the boot conf file
blacklist=b43,ssb,bcma 
Note: boot config file location depends on how you installed tinycore to a USB thumbdrive.  Most likely "extlinux.conf" will be located iin /tce/boot.      If lost, then use the find utility from the terminal to find all config files
sudo find / -iname "*conf"I suggest reading the core  book for valuable insight to core fundamentals 
http://tinycorelinux.net/book.htmlIf you have an Ethernet connection available, you wouldn't need to blacklist the b43 modules, but you would need to cut the firmware from Broadcom's own drivers.  Using firmware-getb43 extension simplifies that task and creates the required firmware extension for you
I strongly recommend the wifi.tcz (extension) over any other wifi connection app.   Honestly I've tried wicd but have always returned to using wifi.tcz extension for long term use.  It's up to you, there are many options.
For wifi,  all that is needed is
wifi.tcz
any modules specific to the hardware
and firmware-(foryourhardware).tcz