How can I wire a Mini-USB to Micro-USB cable?
To solve your problem of interconnect, you need to define the function of your cable. The distinction between "A" and "B" variants (be it classic Type-A or B, or their mini/micro variants) is specifically to determine which one goes to host, and which goes to a device. The cables of this sort must be always of A-B type, not B-B. 

The tablet device, if it is a strictly host, must have Type-A receptacle, micro or normal. To fit in, the cable end must be of squarish Type-uA, with ID pin grounded.

If the tablet has OTG functionality (which is likely), the ID pin ground makes the tablet to turn into HOST mode. If ID is floating, it will/should act as DEVICE.

Now, it become a common practice in tablets to use micro-B receptacles, and not micro A/B, even if the tablet's port has dual-role functionality.  To make such tablet to be a host, people have invented "OTG adapters", which have u-B shape on one end, but has the ID pin grounded , and Type-A receptacle on the other end. Then you can use a standard Type-A to mini-B cable to connect to the old keyboard. Or you can try to solder a u-B connector and ground its ID pin, but it would require the overmold disassembly, and might be difficult. Alternatively you can get a cable with u-A end (square shape), and file off proper corners of its shroud, to make it fit into angled u-B receptacle. Then connect VBUS, GND, D+ and D- to your mini-B keyboard cable.

Since the keyboard is likely a Low-Speed device, no special care or workmanship is required to make this cable connection.