I try to send email to external (internal it's working). I don't know what you mean "your server without a smarthost?"
My server it's conected to WAN (DMZ with public ip address) as well with an internal NIC for internal LAN.
It's full visible on internet.
from log i have:
@4000000053bd09e7272a8704 status: local 1/20 remote 2/20
@4000000053bd09e7272a8aec end msg 30417626
@4000000053bd09e72cbc6e44 new msg 30417626
@4000000053bd09e72cbc79fc info msg 30417626: bytes 31120 from <user@domain.tld> qp 21684 uid 5012
@4000000053bd09e72d9b3584 starting delivery 781: msg 30417626 to local alias-localdelivery-user@domain.tld
@4000000053bd09e72d9b4524 status: local 2/20 remote 2/20
@4000000053bd09e72d9b4cf4 delivery 780: success: did_1+1+1/qp_21684/
@4000000053bd09e72d9b54c4 status: local 1/20 remote 2/20
@4000000053bd09e72da20b84 end msg 30413919
@4000000053bd09e72f966174 new msg 30413919
@4000000053bd09e72f97e42c info msg 30413919: bytes 31242 from <noreply@domain.tld> qp 21687 uid 400
@4000000053bd09e730441634 starting delivery 782: msg 30413919 to local user@www.domain.tld
@4000000053bd09e7304421ec status: local 2/20 remote 2/20
@4000000053bd09e7304673ac delivery 781: success: forward:_qp_21687/did_0+0+1/
@4000000053bd09e7304f7844 status: local 1/20 remote 2/20
@4000000053bd09e7305b7e64 end msg 30417626
@4000000053bd09e73373034c delivery 782: success: did_1+0+1/
@4000000053bd09e7337a276c status: local 0/20 remote 2/20
@4000000053bd09e7337c9c54 end msg 30413919
@4000000053bd0a0402a20ca4 starting delivery 783: msg 30417623 to remote user@domain.tld
@4000000053bd0a0402a25eac status: local 0/20 remote 3/20
@4000000053bd0a0402a26294 starting delivery 784: msg 30417627 to remote user@domain.tld
@4000000053bd0a0402a26a64 status: local 0/20 remote 4/20
@4000000053bd0a0402a27234 starting delivery 785: msg 30417570 to remote user@domain.tld
@4000000053bd0a0402a27a04 status: local 0/20 remote 5/20
@4000000053bd0a0402a27dec starting delivery 786: msg 30412848 to remote user@domain.tld
@4000000053bd0a0402a3d1c4 status: local 0/20 remote 6/20
@4000000053bd0a0402a3d994 starting delivery 787: msg 30417572 to remote user@domain.tld
@4000000053bd0a0402a3dd7c status: local 0/20 remote 7/20
@4000000053bd0a0402a3e54c starting delivery 788: msg 30417648 to remote user@domain.tld
@4000000053bd0a0402a3ed1c status: local 0/20 remote 8/20
@4000000053bd0a0402a3f104 starting delivery 789: msg 30413887 to remote user@domain.tld
@4000000053bd0a0402a45e64 status: local 0/20 remote 9/20
@4000000053bd0a0402a46634 starting delivery 790: msg 30417641 to remote user@domain.tld
@4000000053bd0a0402a46e04 status: local 0/20 remote 10/20
@4000000053bd0a0402a471ec starting delivery 791: msg 30417649 to remote user@domain.tld
@4000000053bd0a0402a4912c status: local 0/20 remote 11/20
@4000000053bd0a0403868104 delivery 784: deferral: Sorry,_I_wasn't_able_to_establish_an_SMTP_connection._(#4.4.1)/
@4000000053bd0a0403868cbc status: local 0/20 remote 10/20
@4000000053bd0a0605531344 delivery 790: deferral: Sorry,_I_wasn't_able_to_establish_an_SMTP_connection._(#4.4.1)/
@4000000053bd0a0605531efc status: local 0/20 remote 9/20
@4000000053bd0a0605620b4c delivery 791: deferral: Sorry,_I_wasn't_able_to_establish_an_SMTP_connection._(#4.4.1)/
@4000000053bd0a060566be6c status: local 0/20 remote 8/20
@4000000053bd0a0905c6a14c delivery 788: deferral: Sorry,_I_wasn't_able_to_establish_an_SMTP_connection._(#4.4.1)/
@4000000053bd0a0905c6ad04 status: local 0/20 remote 7/20
@4000000053bd0a0b229635bc delivery 786: deferral: Sorry,_I_wasn't_able_to_establish_an_SMTP_connection._(#4.4.1)/
@4000000053bd0a0b22964174 status: local 0/20 remote 6/20
@4000000053bd0a17058d6cc4 delivery 785: deferral: CNAME_lookup_failed_temporarily._(#4.4.3)/
@4000000053bd0a17058d7c64 status: local 0/20 remote 5/20
@4000000053bd0a170da49f54 delivery 783: success: 217.115.16.27_accepted_message./Remote_host_said:_250_2.6.0__<53BCED15.2090201@domain.tld>_Queued_mail_for_delivery/
@4000000053bd0a170da4b2dc status: local 0/20 remote 4/20
@4000000053bd0a170da4b6c4 end msg 30417623
@4000000053bd0a1802eb2b64 delivery 787: deferral: CNAME_lookup_failed_temporarily._(#4.4.3)/
@4000000053bd0a1802eb371c status: local 0/20 remote 3/20"
I replace real mails with "user@domain.tld"
Oh, i forget, after few hours all nameservers from resolv.conf disapear, and for that I must write again nameservers in resolv.conf