If you shoot an unarmed man the burden will be on you to show some reason why his fists were deadly
No, you don't have to show that his fists were deadly. You have to show that it's a reasonable belief that his fists presented a threat of serious bodily harm or death.
Want that proof?
Table 2.9
http://www.fbi.gov/ucr/cius_04/offenses_reported/violent_crime/murder.html
Weapons 2000 2001 1 2002 2003 2004
Total 13,230 14,061 14,263 14,465 14,121
Total firearms: 8,661 8,890 9,528 9,659 9,326
Handguns 6,778 6,931 7,294 7,745 7,265
Rifles 411 386 488 392 393
Shotguns 485 511 486 454 507
Other guns 53 59 75 76 117
Firearms, type not stated 934 1,003 1,185 992 1,044
Knives or cutting instruments 1,782 1,831 1,776 1,828 1,866
Blunt objects (clubs, hammers, etc.) 617 680 681 650 663
Personal weapons (hands, fists, feet, etc.) 2 927 961 954 962 933
Poison 8 12 23 9 11
Explosives 9 4 11 4 1
Fire 134 109 103 170 114
Narcotics 20 37 48 44 76
Drowning 15 23 20 17 15
Strangulation 166 153 145 184 155
Asphyxiation 92 116 100 131 105
Other weapons or weapons not stated 799 1,245 874 807 856
1088 people killed by bare handed assailants in 2004. Fists are a deadly weapon.