I have a EYE/Iwasaki 125W mercury lamp which the arctube is COMPLETELY blackened. Jace said here that overdrive a lamp for about 5 min. will "repair" it. Are there any risks of explosion? (Explosion in an Open-bottom won't be very handy...  )

 If you overpower it there is always a chance that it can explode!!

Another way is to put it in HPS ballast with ignitor to kick start it.....Putting a 125 watt in a 175 watt MV ballast MOST likely will not explode.......but again, I can't say it WON'T but the higher wattage fixture, the more chance....

I ran this 100W lamp in a 175W fixture. It still will not start without a kick, but it ran fine for over an hour.It wouldn't stay lit with the 100W ballast, it would shut off when it reached full brightness and not come back on, unless I kick started it once it cooled. B.T.W I used a mogul to medium socket adapter to run it in the 175 W fixture.

Is the adapter rated for the open-circuit voltage of a mercury lamp?

Yes,the adapter is porcelain and it's rated for 250V. The OCV of the 175W merc is aprox. 212V.
A handy adapter for testing.