Basically, mostly not true. Ancient and early medieval Japan imported copper, bronze, and iron, and bronze and iron weapons, from Korea and China, before domestic iron and copper industries were established. Once domestic production was established, Japan became an exporter of copper and weapons.

In more detail:

First, Japanese natural resources:

Iron: By modern industrial standards, Japan is short of iron ore. But modern iron/steel industries are immensely larger than ancient and medieval iron/steel industries. Late Edo Period Japan was producing about 20,000 tons of iron per year, about 1kg of iron per capita, which is about the same per capita production estimates for Song China (1.2kg per capita, but this estimate might be up to twice as high as the real production). The biggest limitation on increasing iron production before industrialisation was the availability of charcoal. European traders did bring iron and steel to Japan (probably mostly from India), but found the prices they could get were not high - Japan was not short of iron.

Copper: Medieval Japan was a major copper producer and exporter (although some of the most productive mines were exhausted by the end of the 17th century). In the early 17th century, Japan was exporting about 2000 tons of copper per year to China alone (which was about 2/3 of the copper China needed each year for coinage), and also exporting copper to Korea and possibly even Europe (in any case, Dutch merchants were buying large amounts of Japanese copper).

Second, weapons:

Imports vs exports: As noted above, ancient Japan imported weapons. Weapons were still imported from China in the early medieval period, but we don't know how important such imports were in terms of quality. The surviving weapons are high-class fancy swords, and may have been imported more as high-status luxury goods rather than for use as weapons. Later, Japan exported weapons. In about a century of trade with Ming China, Japan exported about 128,000 swords to China. Later, Japan exported weapons (and armour, and military manpower) to South-East Asia.

Metal carried by a soldier: For an unarmoured soldier, it's quite possible that the main metal object carried was his weapon (sword, spear, or other polearm). But other metal objects such as knives, coins, and other things would have been carried. An armoured soldier might wear 20kg of metal armour, a pair of swords (about 1.5kg of metal), and a polearm (another 1.5kg of metal). Some armour was rawhide, so not all armoured soldiers carried so much metal (but they'd still be carrying about the same total weight). An unarmoured infantry archer might be the soldier carrying the least metal - perhaps a short sword in addition to arrowheads and the knives, coins, etc. noted above.

The 16th century saw the large scale production of guns, and at the end of the century there might have been about 50,000 guns in Japan (about half of which appeared on the battlefield at Sekigahara). And this was after many tens of thousands of guns - many of which did not come back - went to Korea with Hideyoshi's invasions. But note that 50,000 guns is only about 100 tons of iron, which is not much compared to total annual production in Japan - the limiting factor in production was skilled labour and the willingness to pay for that skilled labour.

All-wood (sticks from short truncheons to 6') and all-bamboo weapons (improvised spears) were used, but were not standard battlefield weapons.