I know this isn't a guitar, but I couldn't work out anywhere else to ask this. It's more about using DI's than microphones anyway.

I use a harmonica 'bullet' type mic on stage for additional vocal effects in some parts of songs, to give it a telephone-like lowfi sound. The mic I have is a Hohner bluesblaster (or something like that) which has an XLR jack on it so you can plug an XLR-1/4" jack cable in to the mic and then into a guitar amp or DI.

Because this is a Hi-Z mic, and so has a Hi-Z cable (with 1/4" jack at the end), does that mean I have to use this mic with the cable to plug into a DI, and then into the mixing desk? Last time I used it, the soundguy insisted on plugging the mic straight in to the mixing desk with an XLR-XLR cable, but he found there to be very low signal coming out of it... (he wouldn't admit that it might be because he didn't use a DI and XLR-1/4" cable)

How should this mic be used for best signal strength? Or does it not matter?
Ideally you should have a HI-Z to Low-Z transformer, or an active DI using a guitar input. If the mixer is stage-side then straight to low Z mic will work but is not ideal. If the mixer is at the end of a multicore then it won't work very well at all. Many new PA guys might not have worked with hi-Z stuff before and may not know how to treat it. Best to get yourself a transformer to use.

I tried to find a suitable one but this is the closest I could get. To got Low to High there are lots available - but these have the wrong plugs and sockets for you (transformers work both ways).

This page tells you all about impedance matching, lead lengths etc.